library(readr)
b_data <- read_csv("/Users/raj/Desktop/Billionaires Statistics Dataset.csv")
## Rows: 197 Columns: 22
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (13): category, personName, country, city, source, industries, countryOf...
## dbl (8): rank, age, finalWorth, birthYear, birthMonth, birthDay, cpi_countr...
## lgl (1): selfMade
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
attach(b_data)
str(b_data)
## spc_tbl_ [197 × 22] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ rank : num [1:197] 1 2 3 4 5 6 7 8 9 10 ...
## $ age : num [1:197] 74 51 59 78 92 67 81 83 65 67 ...
## $ finalWorth : num [1:197] 211000 180000 114000 107000 106000 104000 94500 93000 83400 80700 ...
## $ birthYear : num [1:197] 1949 1971 1964 1944 1930 ...
## $ birthMonth : num [1:197] 3 6 1 8 8 10 2 1 4 3 ...
## $ birthDay : num [1:197] 5 28 12 17 30 28 14 28 19 24 ...
## $ category : chr [1:197] "Fashion & Retail" "Automotive" "Technology" "Technology" ...
## $ personName : chr [1:197] "Bernard Arnault & family" "Elon Musk" "Jeff Bezos" "Larry Ellison" ...
## $ country : chr [1:197] "France" "United States" "United States" "United States" ...
## $ city : chr [1:197] "Paris" "Austin" "Medina" "Lanai" ...
## $ source : chr [1:197] "LVMH" "Tesla, SpaceX" "Amazon" "Oracle" ...
## $ industries : chr [1:197] "Fashion & Retail" "Automotive" "Technology" "Technology" ...
## $ countryOfCitizenship: chr [1:197] "France" "United States" "United States" "United States" ...
## $ organization : chr [1:197] "LVMH Moët Hennessy Louis Vuitton" "Tesla" "Amazon" "Oracle" ...
## $ selfMade : logi [1:197] FALSE TRUE TRUE TRUE TRUE TRUE ...
## $ gender : chr [1:197] "M" "M" "M" "M" ...
## $ birthDate : chr [1:197] "3/5/49 0:00" "6/28/71 0:00" "1/12/64 0:00" "8/17/44 0:00" ...
## $ state : chr [1:197] NA "Texas" "Washington" "Hawaii" ...
## $ residenceStateRegion: chr [1:197] NA "South" "West" "West" ...
## $ cpi_country : num [1:197] 110 117 117 117 117 ...
## $ cpi_change_country : num [1:197] 1.1 7.5 7.5 7.5 7.5 7.5 7.5 3.6 7.7 7.5 ...
## $ gdp_country : chr [1:197] "$2,715,518,274,227.00" "$21,427,700,000,000.00" "$21,427,700,000,000.00" "$21,427,700,000,000.00" ...
## - attr(*, "spec")=
## .. cols(
## .. rank = col_double(),
## .. age = col_double(),
## .. finalWorth = col_double(),
## .. birthYear = col_double(),
## .. birthMonth = col_double(),
## .. birthDay = col_double(),
## .. category = col_character(),
## .. personName = col_character(),
## .. country = col_character(),
## .. city = col_character(),
## .. source = col_character(),
## .. industries = col_character(),
## .. countryOfCitizenship = col_character(),
## .. organization = col_character(),
## .. selfMade = col_logical(),
## .. gender = col_character(),
## .. birthDate = col_character(),
## .. state = col_character(),
## .. residenceStateRegion = col_character(),
## .. cpi_country = col_double(),
## .. cpi_change_country = col_double(),
## .. gdp_country = col_character()
## .. )
## - attr(*, "problems")=<externalptr>
excluded_columns <- c(-4,-5,-6,-7,-8,-9,-10,-11,-12,-13,-14,-15,-16,-17,-18,-19,-20,-21,-22)
#cor(b_data[-4,-5,-6,-7,-8,-9,-10,-11,-12,-13,-14,-15,-16,-17,-18,-19,-20,-21,-22])
result <- cor(b_data[,excluded_columns])
excluded_columns
## [1] -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22
result
## rank age finalWorth
## rank 1.00000000 -0.07913784 -0.70553965
## age -0.07913784 1.00000000 0.02832739
## finalWorth -0.70553965 0.02832739 1.00000000
b_data_pca <- prcomp(b_data[,excluded_columns],scale=TRUE)
b_data_pca
## Standard deviations (1, .., p=3):
## [1] 1.3090613 0.9968619 0.5409481
##
## Rotation (n x k) = (3 x 3):
## PC1 PC2 PC3
## rank 0.7050171 0.03888488 0.7081235
## age -0.1060159 0.99305470 0.0510196
## finalWorth -0.7012215 -0.11104201 0.7042430
summary(b_data_pca)
## Importance of components:
## PC1 PC2 PC3
## Standard deviation 1.3091 0.9969 0.54095
## Proportion of Variance 0.5712 0.3312 0.09754
## Cumulative Proportion 0.5712 0.9025 1.00000
# sample scores stored
(eigen_b_data <- b_data_pca$sdev^2)
## [1] 1.7136414 0.9937337 0.2926249
names(eigen_b_data) <- paste("PC",1:3,sep="")
eigen_b_data
## PC1 PC2 PC3
## 1.7136414 0.9937337 0.2926249
sumlambdas <- sum(eigen_b_data)
sumlambdas
## [1] 3
propvar <- eigen_b_data/sumlambdas
propvar
## PC1 PC2 PC3
## 0.57121381 0.33124456 0.09754163
cumvar_b_data <- cumsum(propvar)
cumvar_b_data
## PC1 PC2 PC3
## 0.5712138 0.9024584 1.0000000
matlambdas <- rbind(eigen_b_data,propvar,cumvar_b_data)
rownames(matlambdas) <- c("Eigenvalues","Prop. variance","Cum. prop. variance")
round(matlambdas,4)
## PC1 PC2 PC3
## Eigenvalues 1.7136 0.9937 0.2926
## Prop. variance 0.5712 0.3312 0.0975
## Cum. prop. variance 0.5712 0.9025 1.0000
summary(b_data_pca)
## Importance of components:
## PC1 PC2 PC3
## Standard deviation 1.3091 0.9969 0.54095
## Proportion of Variance 0.5712 0.3312 0.09754
## Cumulative Proportion 0.5712 0.9025 1.00000
b_data_pca$rotation
## PC1 PC2 PC3
## rank 0.7050171 0.03888488 0.7081235
## age -0.1060159 0.99305470 0.0510196
## finalWorth -0.7012215 -0.11104201 0.7042430
print(b_data_pca)
## Standard deviations (1, .., p=3):
## [1] 1.3090613 0.9968619 0.5409481
##
## Rotation (n x k) = (3 x 3):
## PC1 PC2 PC3
## rank 0.7050171 0.03888488 0.7081235
## age -0.1060159 0.99305470 0.0510196
## finalWorth -0.7012215 -0.11104201 0.7042430
## Sample scores stored in b_data_pca$x
b_data_pca$x
## PC1 PC2 PC3
## [1,] -6.018762029 -0.40221757 3.59191907
## [2,] -5.028184548 -1.94155766 2.71486049
## [3,] -3.373832285 -1.09131018 1.04572055
## [4,] -3.327800487 0.31487183 0.94731796
## [5,] -3.397990109 1.33418580 0.98587088
## [6,] -3.140640833 -0.46865024 0.85329324
## [7,] -2.991383577 0.58541427 0.67145370
## [8,] -2.955827138 0.73716061 0.65236480
## [9,] -2.556421699 -0.52733082 0.34879229
## [10,] -2.489884525 -0.37067853 0.29858916
## [11,] -2.487890549 -0.22424698 0.31320735
## [12,] -2.295032079 -1.59513894 0.22111845
## [13,] -2.519924539 1.09461044 0.32196766
## [14,] -2.180073486 -1.65316685 0.15913931
## [15,] -2.108224408 -0.24289654 0.03480820
## [16,] -1.770885226 -2.40152955 -0.15787072
## [17,] -1.998254628 1.17214065 -0.10309380
## [18,] -1.789370431 -0.78448587 -0.20361828
## [19,] -1.867910453 0.23223606 -0.13196492
## [20,] -1.855572101 0.52769120 -0.13582900
## [21,] -1.781350867 0.16971101 -0.16542268
## [22,] -1.647776087 -0.39994851 -0.24248568
## [23,] -1.470303199 -0.88896378 -0.36768261
## [24,] -1.398602569 -0.73149382 -0.42307143
## [25,] -1.525494151 1.08946142 -0.37208548
## [26,] -1.154732220 -2.24296302 -0.53358463
## [27,] -1.428616386 0.95487756 -0.41185923
## [28,] -1.367233935 1.18440633 -0.46093207
## [29,] -1.321376780 1.11670557 -0.47822609
## [30,] -1.095025704 -0.83842471 -0.57157864
## [31,] -1.260643206 0.97639809 -0.48169990
## [32,] -1.291589013 1.26626868 -0.46680739
## [33,] -1.313392145 1.77612589 -0.42380878
## [34,] -0.898714642 -1.32826602 -0.64155270
## [35,] -1.079813780 0.55779794 -0.54017227
## [36,] -0.901875390 -1.10895799 -0.62580424
## [37,] -0.683848518 -2.84559790 -0.69822262
## [38,] -0.823657472 -1.10038095 -0.63021697
## [39,] -0.945429260 0.35292126 -0.56413958
## [40,] -0.850589131 -0.29656484 -0.59825437
## [41,] -0.895005134 0.35836674 -0.56535284
## [42,] -0.879532230 0.21343144 -0.57279910
## [43,] -0.921962989 0.94110043 -0.52122395
## [44,] -0.891017182 0.65122983 -0.53611647
## [45,] -0.569817245 -1.87969241 -0.66763924
## [46,] -0.885009058 1.31160689 -0.50442819
## [47,] -0.929433793 1.89284433 -0.46747124
## [48,] -0.651483086 -0.34888590 -0.59645912
## [49,] -0.783581785 1.10278099 -0.52001032
## [50,] -0.701641564 0.52494488 -0.54521627
## [51,] -0.555228001 -0.63222360 -0.60280011
## [52,] -0.602225732 0.02229915 -0.56730573
## [53,] -0.442920993 -1.28021345 -0.62974297
## [54,] -0.567291973 0.02529165 -0.55296187
## [55,] -0.591062884 0.60979973 -0.53674773
## [56,] -0.552968378 0.39348420 -0.53815234
## [57,] -0.566447305 0.68485105 -0.51608789
## [58,] -0.342677957 -1.27068806 -0.60684759
## [59,] -0.353566424 -0.90521825 -0.59143143
## [60,] -0.305153738 -1.19359259 -0.59915201
## [61,] -0.519780411 0.98193313 -0.48028622
## [62,] -0.339839313 -0.46469711 -0.55535543
## [63,] -0.291426627 -0.75307146 -0.56307601
## [64,] -0.446743414 0.84230424 -0.47140240
## [65,] -0.426694807 0.84420932 -0.46682332
## [66,] -0.449904162 1.06161226 -0.45565394
## [67,] -0.319559986 0.12170766 -0.48452505
## [68,] -0.384612348 0.92075688 -0.43899155
## [69,] -0.243362241 -0.23722925 -0.49138969
## [70,] -0.231050086 -0.16285653 -0.48308748
## [71,] -0.107854610 -1.17631619 -0.52544651
## [72,] -0.154852340 -0.52179344 -0.48995212
## [73,] -0.201271051 -0.08698755 -0.46761335
## [74,] 0.073492712 -2.33049217 -0.56868649
## [75,] -0.050290516 -1.17100979 -0.50911642
## [76,] -0.084993555 -0.58950258 -0.45720898
## [77,] -0.302201956 1.58561431 -0.33575033
## [78,] -0.201628084 0.64353487 -0.38415101
## [79,] -0.019710474 -0.80405210 -0.43649117
## [80,] -0.113126915 0.28527654 -0.37865801
## [81,] -0.185915729 1.15679341 -0.32940139
## [82,] 0.019816452 -0.50683095 -0.41823284
## [83,] -0.047808905 0.36550358 -0.37416192
## [84,] 0.075386570 -0.64795609 -0.41652094
## [85,] 0.106332377 -0.93782669 -0.43141346
## [86,] 0.002001273 0.29588935 -0.34599785
## [87,] 0.118048049 -0.79112538 -0.40184479
## [88,] 0.147818351 -0.78895054 -0.38231522
## [89,] 0.010556196 0.66189869 -0.30068072
## [90,] 0.103393617 -0.20771310 -0.34535826
## [91,] 0.064711358 0.15462514 -0.32674262
## [92,] 0.184158334 -0.49350378 -0.33614214
## [93,] 0.119105972 0.30554544 -0.29060865
## [94,] 0.182991561 -0.12776421 -0.30577549
## [95,] 0.020526075 1.39405642 -0.22758979
## [96,] 0.128836399 0.37950934 -0.27971359
## [97,] 0.036808718 1.61390397 -0.18194035
## [98,] 0.090963880 1.10663043 -0.20800225
## [99,] 0.053687845 1.76142293 -0.15755738
## [100,] 0.246520118 0.16944856 -0.23748000
## [101,] 0.248514094 0.31588011 -0.22286181
## [102,] 0.380033774 -0.91606992 -0.28615500
## [103,] 0.278284397 0.31805495 -0.20333225
## [104,] 0.269960193 0.53654532 -0.18239808
## [105,] 0.331851807 -0.04319588 -0.21218311
## [106,] 0.454459531 -0.91063283 -0.23733109
## [107,] 0.376507261 -0.03993362 -0.18288877
## [108,] 0.267609185 1.12063619 -0.11355393
## [109,] 0.321764347 0.61336264 -0.13961583
## [110,] 0.445769562 -0.03531418 -0.12887916
## [111,] 0.630856651 -1.62851504 -0.20102321
## [112,] 0.470385141 0.03973714 -0.10821932
## [113,] 0.578107713 -0.82878723 -0.14313208
## [114,] 0.389272123 1.12974437 -0.03802853
## [115,] 0.404745027 0.98480907 -0.04547479
## [116,] 0.455142957 0.76917213 -0.03452176
## [117,] 0.547392625 0.04558306 -0.06198827
## [118,] 0.624169391 -0.53307071 -0.08200852
## [119,] 0.646790994 -0.60445094 -0.07596686
## [120,] 0.584311628 0.12131297 -0.02897080
## [121,] 0.398049034 2.00655926 0.07759534
## [122,] 0.722392255 -0.89105928 -0.06156504
## [123,] 0.645027737 -0.16638279 -0.02433375
## [124,] 0.455595663 1.86447739 0.10203627
## [125,] 0.671628560 -0.01859406 0.01499970
## [126,] 0.763878228 -0.74218313 -0.01246680
## [127,] 0.477629514 1.93911988 0.12528896
## [128,] 0.631183045 0.78181233 0.08524846
## [129,] 0.646655948 0.63687704 0.07780221
## [130,] 0.871013049 -1.46468479 -0.03016853
## [131,] 0.662947323 0.93041872 0.11939621
## [132,] 0.662947323 0.93041872 0.11939621
## [133,] 0.732575389 0.27820988 0.08588805
## [134,] 0.857168356 -0.51648966 0.07941368
## [135,] 0.639959955 1.65862723 0.20087233
## [136,] 0.858574580 -0.22403540 0.11124291
## [137,] 0.773473611 0.57310874 0.15219733
## [138,] 0.937345321 -0.65625762 0.10584085
## [139,] 0.965130380 -0.72682019 0.10669679
## [140,] 1.034170693 -1.23300632 0.09039967
## [141,] 0.887178110 0.14387901 0.16113912
## [142,] 0.891157330 0.36304797 0.19443092
## [143,] 1.006616354 -0.57794405 0.15579503
## [144,] 0.714625163 2.32225816 0.31189211
## [145,] 0.863611722 1.09180438 0.25577085
## [146,] 1.218900750 -2.09568476 0.10171796
## [147,] 0.948124939 0.44068296 0.23202747
## [148,] 0.948124939 0.44068296 0.23202747
## [149,] 1.095927262 -0.57141953 0.21438371
## [150,] 1.165555327 -1.22362837 0.18087555
## [151,] 1.007069060 0.51736121 0.29235306
## [152,] 1.045751319 0.15502297 0.27373742
## [153,] 1.099906481 -0.35225058 0.24767551
## [154,] 1.138588740 -0.71458882 0.22905987
## [155,] 0.953135885 1.53544032 0.38872169
## [156,] 1.076919113 0.37595793 0.32915163
## [157,] 1.212418012 -0.63682315 0.29915024
## [158,] 1.266573174 -1.14409669 0.27308834
## [159,] 1.046195293 1.17663409 0.41435088
## [160,] 1.030722390 1.32156939 0.42179713
## [161,] 1.169978521 0.01715170 0.35478082
## [162,] 1.010904502 1.90416401 0.48346936
## [163,] 1.118627074 1.03563964 0.44855660
## [164,] 1.180518688 0.45589844 0.41877157
## [165,] 1.331490491 -0.70181793 0.38132392
## [166,] 1.470746622 -2.00623561 0.31430760
## [167,] 1.424327912 -1.57142972 0.33664637
## [168,] 1.272990344 0.24311493 0.46161179
## [169,] 1.496759692 -1.71242417 0.37085209
## [170,] 1.365240013 -0.48047414 0.43414528
## [171,] 1.195038075 1.11381414 0.51605412
## [172,] 1.334294206 -0.19060354 0.44903780
## [173,] 1.256929689 0.53407295 0.48626908
## [174,] 1.512232596 -1.85735947 0.36340583
## [175,] 1.380712916 -0.62540944 0.42669902
## [176,] 1.256929689 0.53407295 0.48626908
## [177,] 1.597768807 -1.70658663 0.46712031
## [178,] 1.303783641 1.04718404 0.60859920
## [179,] 1.473985580 -0.54710424 0.52669037
## [180,] 1.312329833 1.33949923 0.65797176
## [181,] 1.412315953 0.54344251 0.62678213
## [182,] 1.427201104 0.54452993 0.63654691
## [183,] 1.380782394 0.97933583 0.65888568
## [184,] 1.605139494 -1.12222600 0.55091495
## [185,] 1.589666591 -0.97729070 0.55836120
## [186,] 1.574193687 -0.83235540 0.56580746
## [187,] 1.419464653 0.61699758 0.64027004
## [188,] 1.588704342 -0.24813384 0.66714544
## [189,] 1.619650149 -0.53800444 0.65225292
## [190,] 1.666068859 -0.97281033 0.62991415
## [191,] 1.488130469 0.69394560 0.71554612
## [192,] 1.580967890 -0.17566619 0.67086857
## [193,] 1.598648024 0.26294148 0.75240266
## [194,] 1.598648024 0.26294148 0.75240266
## [195,] 1.621857380 0.04553853 0.74123327
## [196,] 1.691485445 -0.60667031 0.70772511
## [197,] 1.660539638 -0.31679971 0.72261763
# Identifying the scores by their selfMade status
b_datatyp_pca <- cbind(data.frame(selfMade),b_data_pca$x)
print(b_datatyp_pca)
## selfMade PC1 PC2 PC3
## 1 FALSE -6.018762029 -0.40221757 3.59191907
## 2 TRUE -5.028184548 -1.94155766 2.71486049
## 3 TRUE -3.373832285 -1.09131018 1.04572055
## 4 TRUE -3.327800487 0.31487183 0.94731796
## 5 TRUE -3.397990109 1.33418580 0.98587088
## 6 TRUE -3.140640833 -0.46865024 0.85329324
## 7 TRUE -2.991383577 0.58541427 0.67145370
## 8 TRUE -2.955827138 0.73716061 0.65236480
## 9 FALSE -2.556421699 -0.52733082 0.34879229
## 10 TRUE -2.489884525 -0.37067853 0.29858916
## 11 FALSE -2.487890549 -0.22424698 0.31320735
## 12 TRUE -2.295032079 -1.59513894 0.22111845
## 13 TRUE -2.519924539 1.09461044 0.32196766
## 14 TRUE -2.180073486 -1.65316685 0.15913931
## 15 TRUE -2.108224408 -0.24289654 0.03480820
## 16 TRUE -1.770885226 -2.40152955 -0.15787072
## 17 FALSE -1.998254628 1.17214065 -0.10309380
## 18 FALSE -1.789370431 -0.78448587 -0.20361828
## 19 FALSE -1.867910453 0.23223606 -0.13196492
## 20 FALSE -1.855572101 0.52769120 -0.13582900
## 21 FALSE -1.781350867 0.16971101 -0.16542268
## 22 FALSE -1.647776087 -0.39994851 -0.24248568
## 23 TRUE -1.470303199 -0.88896378 -0.36768261
## 24 TRUE -1.398602569 -0.73149382 -0.42307143
## 25 TRUE -1.525494151 1.08946142 -0.37208548
## 26 TRUE -1.154732220 -2.24296302 -0.53358463
## 27 FALSE -1.428616386 0.95487756 -0.41185923
## 28 TRUE -1.367233935 1.18440633 -0.46093207
## 29 FALSE -1.321376780 1.11670557 -0.47822609
## 30 FALSE -1.095025704 -0.83842471 -0.57157864
## 31 FALSE -1.260643206 0.97639809 -0.48169990
## 32 FALSE -1.291589013 1.26626868 -0.46680739
## 33 TRUE -1.313392145 1.77612589 -0.42380878
## 34 TRUE -0.898714642 -1.32826602 -0.64155270
## 35 FALSE -1.079813780 0.55779794 -0.54017227
## 36 TRUE -0.901875390 -1.10895799 -0.62580424
## 37 FALSE -0.683848518 -2.84559790 -0.69822262
## 38 TRUE -0.823657472 -1.10038095 -0.63021697
## 39 TRUE -0.945429260 0.35292126 -0.56413958
## 40 TRUE -0.850589131 -0.29656484 -0.59825437
## 41 FALSE -0.895005134 0.35836674 -0.56535284
## 42 FALSE -0.879532230 0.21343144 -0.57279910
## 43 TRUE -0.921962989 0.94110043 -0.52122395
## 44 TRUE -0.891017182 0.65122983 -0.53611647
## 45 TRUE -0.569817245 -1.87969241 -0.66763924
## 46 TRUE -0.885009058 1.31160689 -0.50442819
## 47 TRUE -0.929433793 1.89284433 -0.46747124
## 48 TRUE -0.651483086 -0.34888590 -0.59645912
## 49 TRUE -0.783581785 1.10278099 -0.52001032
## 50 TRUE -0.701641564 0.52494488 -0.54521627
## 51 FALSE -0.555228001 -0.63222360 -0.60280011
## 52 FALSE -0.602225732 0.02229915 -0.56730573
## 53 TRUE -0.442920993 -1.28021345 -0.62974297
## 54 FALSE -0.567291973 0.02529165 -0.55296187
## 55 TRUE -0.591062884 0.60979973 -0.53674773
## 56 TRUE -0.552968378 0.39348420 -0.53815234
## 57 TRUE -0.566447305 0.68485105 -0.51608789
## 58 TRUE -0.342677957 -1.27068806 -0.60684759
## 59 FALSE -0.353566424 -0.90521825 -0.59143143
## 60 FALSE -0.305153738 -1.19359259 -0.59915201
## 61 FALSE -0.519780411 0.98193313 -0.48028622
## 62 TRUE -0.339839313 -0.46469711 -0.55535543
## 63 TRUE -0.291426627 -0.75307146 -0.56307601
## 64 TRUE -0.446743414 0.84230424 -0.47140240
## 65 FALSE -0.426694807 0.84420932 -0.46682332
## 66 FALSE -0.449904162 1.06161226 -0.45565394
## 67 TRUE -0.319559986 0.12170766 -0.48452505
## 68 FALSE -0.384612348 0.92075688 -0.43899155
## 69 TRUE -0.243362241 -0.23722925 -0.49138969
## 70 TRUE -0.231050086 -0.16285653 -0.48308748
## 71 FALSE -0.107854610 -1.17631619 -0.52544651
## 72 FALSE -0.154852340 -0.52179344 -0.48995212
## 73 TRUE -0.201271051 -0.08698755 -0.46761335
## 74 FALSE 0.073492712 -2.33049217 -0.56868649
## 75 TRUE -0.050290516 -1.17100979 -0.50911642
## 76 TRUE -0.084993555 -0.58950258 -0.45720898
## 77 FALSE -0.302201956 1.58561431 -0.33575033
## 78 TRUE -0.201628084 0.64353487 -0.38415101
## 79 TRUE -0.019710474 -0.80405210 -0.43649117
## 80 TRUE -0.113126915 0.28527654 -0.37865801
## 81 TRUE -0.185915729 1.15679341 -0.32940139
## 82 TRUE 0.019816452 -0.50683095 -0.41823284
## 83 TRUE -0.047808905 0.36550358 -0.37416192
## 84 TRUE 0.075386570 -0.64795609 -0.41652094
## 85 TRUE 0.106332377 -0.93782669 -0.43141346
## 86 FALSE 0.002001273 0.29588935 -0.34599785
## 87 TRUE 0.118048049 -0.79112538 -0.40184479
## 88 TRUE 0.147818351 -0.78895054 -0.38231522
## 89 TRUE 0.010556196 0.66189869 -0.30068072
## 90 TRUE 0.103393617 -0.20771310 -0.34535826
## 91 TRUE 0.064711358 0.15462514 -0.32674262
## 92 TRUE 0.184158334 -0.49350378 -0.33614214
## 93 FALSE 0.119105972 0.30554544 -0.29060865
## 94 TRUE 0.182991561 -0.12776421 -0.30577549
## 95 TRUE 0.020526075 1.39405642 -0.22758979
## 96 FALSE 0.128836399 0.37950934 -0.27971359
## 97 TRUE 0.036808718 1.61390397 -0.18194035
## 98 TRUE 0.090963880 1.10663043 -0.20800225
## 99 FALSE 0.053687845 1.76142293 -0.15755738
## 100 FALSE 0.246520118 0.16944856 -0.23748000
## 101 FALSE 0.248514094 0.31588011 -0.22286181
## 102 FALSE 0.380033774 -0.91606992 -0.28615500
## 103 TRUE 0.278284397 0.31805495 -0.20333225
## 104 FALSE 0.269960193 0.53654532 -0.18239808
## 105 TRUE 0.331851807 -0.04319588 -0.21218311
## 106 TRUE 0.454459531 -0.91063283 -0.23733109
## 107 TRUE 0.376507261 -0.03993362 -0.18288877
## 108 TRUE 0.267609185 1.12063619 -0.11355393
## 109 FALSE 0.321764347 0.61336264 -0.13961583
## 110 TRUE 0.445769562 -0.03531418 -0.12887916
## 111 TRUE 0.630856651 -1.62851504 -0.20102321
## 112 TRUE 0.470385141 0.03973714 -0.10821932
## 113 TRUE 0.578107713 -0.82878723 -0.14313208
## 114 FALSE 0.389272123 1.12974437 -0.03802853
## 115 TRUE 0.404745027 0.98480907 -0.04547479
## 116 TRUE 0.455142957 0.76917213 -0.03452176
## 117 FALSE 0.547392625 0.04558306 -0.06198827
## 118 TRUE 0.624169391 -0.53307071 -0.08200852
## 119 TRUE 0.646790994 -0.60445094 -0.07596686
## 120 TRUE 0.584311628 0.12131297 -0.02897080
## 121 TRUE 0.398049034 2.00655926 0.07759534
## 122 FALSE 0.722392255 -0.89105928 -0.06156504
## 123 TRUE 0.645027737 -0.16638279 -0.02433375
## 124 FALSE 0.455595663 1.86447739 0.10203627
## 125 FALSE 0.671628560 -0.01859406 0.01499970
## 126 TRUE 0.763878228 -0.74218313 -0.01246680
## 127 TRUE 0.477629514 1.93911988 0.12528896
## 128 TRUE 0.631183045 0.78181233 0.08524846
## 129 TRUE 0.646655948 0.63687704 0.07780221
## 130 TRUE 0.871013049 -1.46468479 -0.03016853
## 131 TRUE 0.662947323 0.93041872 0.11939621
## 132 FALSE 0.662947323 0.93041872 0.11939621
## 133 TRUE 0.732575389 0.27820988 0.08588805
## 134 TRUE 0.857168356 -0.51648966 0.07941368
## 135 TRUE 0.639959955 1.65862723 0.20087233
## 136 TRUE 0.858574580 -0.22403540 0.11124291
## 137 TRUE 0.773473611 0.57310874 0.15219733
## 138 TRUE 0.937345321 -0.65625762 0.10584085
## 139 TRUE 0.965130380 -0.72682019 0.10669679
## 140 TRUE 1.034170693 -1.23300632 0.09039967
## 141 TRUE 0.887178110 0.14387901 0.16113912
## 142 TRUE 0.891157330 0.36304797 0.19443092
## 143 FALSE 1.006616354 -0.57794405 0.15579503
## 144 TRUE 0.714625163 2.32225816 0.31189211
## 145 TRUE 0.863611722 1.09180438 0.25577085
## 146 TRUE 1.218900750 -2.09568476 0.10171796
## 147 TRUE 0.948124939 0.44068296 0.23202747
## 148 TRUE 0.948124939 0.44068296 0.23202747
## 149 TRUE 1.095927262 -0.57141953 0.21438371
## 150 TRUE 1.165555327 -1.22362837 0.18087555
## 151 TRUE 1.007069060 0.51736121 0.29235306
## 152 TRUE 1.045751319 0.15502297 0.27373742
## 153 FALSE 1.099906481 -0.35225058 0.24767551
## 154 TRUE 1.138588740 -0.71458882 0.22905987
## 155 TRUE 0.953135885 1.53544032 0.38872169
## 156 FALSE 1.076919113 0.37595793 0.32915163
## 157 TRUE 1.212418012 -0.63682315 0.29915024
## 158 TRUE 1.266573174 -1.14409669 0.27308834
## 159 FALSE 1.046195293 1.17663409 0.41435088
## 160 TRUE 1.030722390 1.32156939 0.42179713
## 161 FALSE 1.169978521 0.01715170 0.35478082
## 162 FALSE 1.010904502 1.90416401 0.48346936
## 163 TRUE 1.118627074 1.03563964 0.44855660
## 164 TRUE 1.180518688 0.45589844 0.41877157
## 165 TRUE 1.331490491 -0.70181793 0.38132392
## 166 TRUE 1.470746622 -2.00623561 0.31430760
## 167 TRUE 1.424327912 -1.57142972 0.33664637
## 168 TRUE 1.272990344 0.24311493 0.46161179
## 169 TRUE 1.496759692 -1.71242417 0.37085209
## 170 FALSE 1.365240013 -0.48047414 0.43414528
## 171 TRUE 1.195038075 1.11381414 0.51605412
## 172 TRUE 1.334294206 -0.19060354 0.44903780
## 173 TRUE 1.256929689 0.53407295 0.48626908
## 174 TRUE 1.512232596 -1.85735947 0.36340583
## 175 FALSE 1.380712916 -0.62540944 0.42669902
## 176 FALSE 1.256929689 0.53407295 0.48626908
## 177 TRUE 1.597768807 -1.70658663 0.46712031
## 178 FALSE 1.303783641 1.04718404 0.60859920
## 179 TRUE 1.473985580 -0.54710424 0.52669037
## 180 TRUE 1.312329833 1.33949923 0.65797176
## 181 TRUE 1.412315953 0.54344251 0.62678213
## 182 TRUE 1.427201104 0.54452993 0.63654691
## 183 FALSE 1.380782394 0.97933583 0.65888568
## 184 FALSE 1.605139494 -1.12222600 0.55091495
## 185 FALSE 1.589666591 -0.97729070 0.55836120
## 186 FALSE 1.574193687 -0.83235540 0.56580746
## 187 TRUE 1.419464653 0.61699758 0.64027004
## 188 TRUE 1.588704342 -0.24813384 0.66714544
## 189 TRUE 1.619650149 -0.53800444 0.65225292
## 190 TRUE 1.666068859 -0.97281033 0.62991415
## 191 FALSE 1.488130469 0.69394560 0.71554612
## 192 TRUE 1.580967890 -0.17566619 0.67086857
## 193 FALSE 1.598648024 0.26294148 0.75240266
## 194 TRUE 1.598648024 0.26294148 0.75240266
## 195 TRUE 1.621857380 0.04553853 0.74123327
## 196 FALSE 1.691485445 -0.60667031 0.70772511
## 197 FALSE 1.660539638 -0.31679971 0.72261763
# Means of scores for all the PC's classified by selfMade status
tabmeansPC <- aggregate(b_datatyp_pca[,2:4],by=list(selfMade=selfMade),mean)
tabmeansPC
## selfMade PC1 PC2 PC3
## 1 FALSE -0.11045638 0.12230507 -0.016949947
## 2 TRUE 0.05315194 -0.05885357 0.008156365
tabmeansPC <- tabmeansPC[rev(order(tabmeansPC$selfMade)),]
tabmeansPC
## selfMade PC1 PC2 PC3
## 2 TRUE 0.05315194 -0.05885357 0.008156365
## 1 FALSE -0.11045638 0.12230507 -0.016949947
excluded_columns_2 <- c(-5,-6,-7,-8,-9,-10,-11,-12,-13,-14,-15,-16,-17,-18,-19,-20,-21,-22)
tabfmeans <- t(tabmeansPC[,excluded_columns_2])
tabfmeans
## 2 1
## selfMade 1.000000000 0.00000000
## PC1 0.053151944 -0.11045638
## PC2 -0.058853566 0.12230507
## PC3 0.008156365 -0.01694995
colnames(tabfmeans) <- t(as.vector(tabmeansPC[1]$selfMade))
tabfmeans
## TRUE FALSE
## selfMade 1.000000000 0.00000000
## PC1 0.053151944 -0.11045638
## PC2 -0.058853566 0.12230507
## PC3 0.008156365 -0.01694995
#Question 1
#Decide how many Principal Components (PCs) you want to keep and why (2 points)
#For this I am taking PC1 and PC2, because I need to calculate the rank based on age.
# Standard deviations of scores for all the PC's classified by selfmade status
tabsdsPC <- aggregate(b_datatyp_pca[,2:4],by=list(selfMade=selfMade),sd)
tabsdsPC
## selfMade PC1 PC2 PC3
## 1 FALSE 1.369311 0.9420996 0.6316469
## 2 TRUE 1.280954 1.0203907 0.4938381
tabfsds <- t(tabsdsPC[,excluded_columns])
colnames(tabfsds) <- t(as.vector(tabsdsPC[1]$selfMade))
tabfsds
## FALSE TRUE
## selfMade 0.0000000 1.000000
## PC1 1.3693110 1.280954
## PC2 0.9420996 1.020391
t.test(PC1~b_data$selfMade,data=b_datatyp_pca)
##
## Welch Two Sample t-test
##
## data: PC1 by b_data$selfMade
## t = -0.80183, df = 117.3, p-value = 0.4243
## alternative hypothesis: true difference in means between group FALSE and group TRUE is not equal to 0
## 95 percent confidence interval:
## -0.5676973 0.2404806
## sample estimates:
## mean in group FALSE mean in group TRUE
## -0.11045638 0.05315194
t.test(PC2~b_data$selfMade,data=b_datatyp_pca)
##
## Welch Two Sample t-test
##
## data: PC2 by b_data$selfMade
## t = 1.2299, df = 133.85, p-value = 0.2209
## alternative hypothesis: true difference in means between group FALSE and group TRUE is not equal to 0
## 95 percent confidence interval:
## -0.1101731 0.4724904
## sample estimates:
## mean in group FALSE mean in group TRUE
## 0.12230507 -0.05885357
#t.test(PC3~b_data$selfMade,data=b_datatyp_pca)
## F ratio tests
var.test(PC1~b_data$selfMade,data=b_datatyp_pca)
##
## F test to compare two variances
##
## data: PC1 by b_data$selfMade
## F = 1.1427, num df = 63, denom df = 132, p-value = 0.5192
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.757440 1.781229
## sample estimates:
## ratio of variances
## 1.142713
var.test(PC2~b_data$selfMade,data=b_datatyp_pca)
##
## F test to compare two variances
##
## data: PC2 by b_data$selfMade
## F = 0.85243, num df = 63, denom df = 132, p-value = 0.4824
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
## 0.5650306 1.3287504
## sample estimates:
## ratio of variances
## 0.8524339
#var.test(PC3~b_data$selfMade,data=b_datatyp_pca)
# Levene's tests (one-sided)
library(car)
## Loading required package: carData
(LTPC1 <- leveneTest(PC1~b_data$selfMade,data=b_datatyp_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 0.3328 0.5647
## 195
(p_PC1_1sided <- LTPC1[[3]][1]/2)
## [1] 0.2823514
(LTPC2 <- leveneTest(PC2~b_data$selfMade,data=b_datatyp_pca))
## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 1.2915 0.2572
## 195
(p_PC2_1sided=LTPC2[[3]][1]/2)
## [1] 0.128584
#(LTPC3 <- leveneTest(PC3~b_data$selfMade,data=b_datatyp_pca))
#(p_PC3_1sided <- LTPC3[[3]][1]/2)
b_data
## # A tibble: 197 × 22
## rank age finalWorth birthYear birthMonth birthDay category personName
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr> <chr>
## 1 1 74 211000 1949 3 5 Fashion & Re… Bernard A…
## 2 2 51 180000 1971 6 28 Automotive Elon Musk
## 3 3 59 114000 1964 1 12 Technology Jeff Bezos
## 4 4 78 107000 1944 8 17 Technology Larry Ell…
## 5 5 92 106000 1930 8 30 Finance & In… Warren Bu…
## 6 6 67 104000 1955 10 28 Technology Bill Gates
## 7 7 81 94500 1942 2 14 Media & Ente… Michael B…
## 8 8 83 93000 1940 1 28 Telecom Carlos Sl…
## 9 9 65 83400 1957 4 19 Diversified Mukesh Am…
## 10 10 67 80700 1956 3 24 Technology Steve Bal…
## # ℹ 187 more rows
## # ℹ 14 more variables: country <chr>, city <chr>, source <chr>,
## # industries <chr>, countryOfCitizenship <chr>, organization <chr>,
## # selfMade <lgl>, gender <chr>, birthDate <chr>, state <chr>,
## # residenceStateRegion <chr>, cpi_country <dbl>, cpi_change_country <dbl>,
## # gdp_country <chr>
# Plotting the scores for the first and second components
plot(b_datatyp_pca$PC1, b_datatyp_pca$PC2,pch=ifelse(b_data_pca$selfMade == "True",1,16),xlab="PC1", ylab="PC2", main="133 Trues using PC1 & PC2")
abline(h=0)
abline(v=0)
legend("bottomleft", legend=c("True","False"), pch=c(1,16))
plot(eigen_b_data, xlab = "Component number", ylab = "Component variance", type = "l", main = "Scree diagram")
plot(log(eigen_b_data), xlab = "Component number",ylab = "log(Component variance)", type="l",main = "Log(eigenvalue) diagram")
print(summary(b_datatyp_pca))
## selfMade PC1 PC2 PC3
## Mode :logical Min. :-6.0188 Min. :-2.84560 Min. :-0.69822
## FALSE:64 1st Qu.:-0.6022 1st Qu.:-0.70182 1st Qu.:-0.43649
## TRUE :133 Median : 0.1842 Median : 0.04554 Median :-0.08201
## Mean : 0.0000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 1.0071 3rd Qu.: 0.68485 3rd Qu.: 0.32197
## Max. : 1.6915 Max. : 2.32226 Max. : 3.59192
# Assuming b_data_pca$x is a data frame or matrix
cov_matrix <- cov(b_data_pca$x)
# Extracting the diagonal elements
diagonal_cov <- diag(cov_matrix)
diag(cov(b_data_pca$x))
## PC1 PC2 PC3
## 1.7136414 0.9937337 0.2926249
xlim <- range(b_data_pca$x[,excluded_columns_2])
b_data_pca$x[,excluded_columns_2]
## PC1 PC2 PC3
## [1,] -6.018762029 -0.40221757 3.59191907
## [2,] -5.028184548 -1.94155766 2.71486049
## [3,] -3.373832285 -1.09131018 1.04572055
## [4,] -3.327800487 0.31487183 0.94731796
## [5,] -3.397990109 1.33418580 0.98587088
## [6,] -3.140640833 -0.46865024 0.85329324
## [7,] -2.991383577 0.58541427 0.67145370
## [8,] -2.955827138 0.73716061 0.65236480
## [9,] -2.556421699 -0.52733082 0.34879229
## [10,] -2.489884525 -0.37067853 0.29858916
## [11,] -2.487890549 -0.22424698 0.31320735
## [12,] -2.295032079 -1.59513894 0.22111845
## [13,] -2.519924539 1.09461044 0.32196766
## [14,] -2.180073486 -1.65316685 0.15913931
## [15,] -2.108224408 -0.24289654 0.03480820
## [16,] -1.770885226 -2.40152955 -0.15787072
## [17,] -1.998254628 1.17214065 -0.10309380
## [18,] -1.789370431 -0.78448587 -0.20361828
## [19,] -1.867910453 0.23223606 -0.13196492
## [20,] -1.855572101 0.52769120 -0.13582900
## [21,] -1.781350867 0.16971101 -0.16542268
## [22,] -1.647776087 -0.39994851 -0.24248568
## [23,] -1.470303199 -0.88896378 -0.36768261
## [24,] -1.398602569 -0.73149382 -0.42307143
## [25,] -1.525494151 1.08946142 -0.37208548
## [26,] -1.154732220 -2.24296302 -0.53358463
## [27,] -1.428616386 0.95487756 -0.41185923
## [28,] -1.367233935 1.18440633 -0.46093207
## [29,] -1.321376780 1.11670557 -0.47822609
## [30,] -1.095025704 -0.83842471 -0.57157864
## [31,] -1.260643206 0.97639809 -0.48169990
## [32,] -1.291589013 1.26626868 -0.46680739
## [33,] -1.313392145 1.77612589 -0.42380878
## [34,] -0.898714642 -1.32826602 -0.64155270
## [35,] -1.079813780 0.55779794 -0.54017227
## [36,] -0.901875390 -1.10895799 -0.62580424
## [37,] -0.683848518 -2.84559790 -0.69822262
## [38,] -0.823657472 -1.10038095 -0.63021697
## [39,] -0.945429260 0.35292126 -0.56413958
## [40,] -0.850589131 -0.29656484 -0.59825437
## [41,] -0.895005134 0.35836674 -0.56535284
## [42,] -0.879532230 0.21343144 -0.57279910
## [43,] -0.921962989 0.94110043 -0.52122395
## [44,] -0.891017182 0.65122983 -0.53611647
## [45,] -0.569817245 -1.87969241 -0.66763924
## [46,] -0.885009058 1.31160689 -0.50442819
## [47,] -0.929433793 1.89284433 -0.46747124
## [48,] -0.651483086 -0.34888590 -0.59645912
## [49,] -0.783581785 1.10278099 -0.52001032
## [50,] -0.701641564 0.52494488 -0.54521627
## [51,] -0.555228001 -0.63222360 -0.60280011
## [52,] -0.602225732 0.02229915 -0.56730573
## [53,] -0.442920993 -1.28021345 -0.62974297
## [54,] -0.567291973 0.02529165 -0.55296187
## [55,] -0.591062884 0.60979973 -0.53674773
## [56,] -0.552968378 0.39348420 -0.53815234
## [57,] -0.566447305 0.68485105 -0.51608789
## [58,] -0.342677957 -1.27068806 -0.60684759
## [59,] -0.353566424 -0.90521825 -0.59143143
## [60,] -0.305153738 -1.19359259 -0.59915201
## [61,] -0.519780411 0.98193313 -0.48028622
## [62,] -0.339839313 -0.46469711 -0.55535543
## [63,] -0.291426627 -0.75307146 -0.56307601
## [64,] -0.446743414 0.84230424 -0.47140240
## [65,] -0.426694807 0.84420932 -0.46682332
## [66,] -0.449904162 1.06161226 -0.45565394
## [67,] -0.319559986 0.12170766 -0.48452505
## [68,] -0.384612348 0.92075688 -0.43899155
## [69,] -0.243362241 -0.23722925 -0.49138969
## [70,] -0.231050086 -0.16285653 -0.48308748
## [71,] -0.107854610 -1.17631619 -0.52544651
## [72,] -0.154852340 -0.52179344 -0.48995212
## [73,] -0.201271051 -0.08698755 -0.46761335
## [74,] 0.073492712 -2.33049217 -0.56868649
## [75,] -0.050290516 -1.17100979 -0.50911642
## [76,] -0.084993555 -0.58950258 -0.45720898
## [77,] -0.302201956 1.58561431 -0.33575033
## [78,] -0.201628084 0.64353487 -0.38415101
## [79,] -0.019710474 -0.80405210 -0.43649117
## [80,] -0.113126915 0.28527654 -0.37865801
## [81,] -0.185915729 1.15679341 -0.32940139
## [82,] 0.019816452 -0.50683095 -0.41823284
## [83,] -0.047808905 0.36550358 -0.37416192
## [84,] 0.075386570 -0.64795609 -0.41652094
## [85,] 0.106332377 -0.93782669 -0.43141346
## [86,] 0.002001273 0.29588935 -0.34599785
## [87,] 0.118048049 -0.79112538 -0.40184479
## [88,] 0.147818351 -0.78895054 -0.38231522
## [89,] 0.010556196 0.66189869 -0.30068072
## [90,] 0.103393617 -0.20771310 -0.34535826
## [91,] 0.064711358 0.15462514 -0.32674262
## [92,] 0.184158334 -0.49350378 -0.33614214
## [93,] 0.119105972 0.30554544 -0.29060865
## [94,] 0.182991561 -0.12776421 -0.30577549
## [95,] 0.020526075 1.39405642 -0.22758979
## [96,] 0.128836399 0.37950934 -0.27971359
## [97,] 0.036808718 1.61390397 -0.18194035
## [98,] 0.090963880 1.10663043 -0.20800225
## [99,] 0.053687845 1.76142293 -0.15755738
## [100,] 0.246520118 0.16944856 -0.23748000
## [101,] 0.248514094 0.31588011 -0.22286181
## [102,] 0.380033774 -0.91606992 -0.28615500
## [103,] 0.278284397 0.31805495 -0.20333225
## [104,] 0.269960193 0.53654532 -0.18239808
## [105,] 0.331851807 -0.04319588 -0.21218311
## [106,] 0.454459531 -0.91063283 -0.23733109
## [107,] 0.376507261 -0.03993362 -0.18288877
## [108,] 0.267609185 1.12063619 -0.11355393
## [109,] 0.321764347 0.61336264 -0.13961583
## [110,] 0.445769562 -0.03531418 -0.12887916
## [111,] 0.630856651 -1.62851504 -0.20102321
## [112,] 0.470385141 0.03973714 -0.10821932
## [113,] 0.578107713 -0.82878723 -0.14313208
## [114,] 0.389272123 1.12974437 -0.03802853
## [115,] 0.404745027 0.98480907 -0.04547479
## [116,] 0.455142957 0.76917213 -0.03452176
## [117,] 0.547392625 0.04558306 -0.06198827
## [118,] 0.624169391 -0.53307071 -0.08200852
## [119,] 0.646790994 -0.60445094 -0.07596686
## [120,] 0.584311628 0.12131297 -0.02897080
## [121,] 0.398049034 2.00655926 0.07759534
## [122,] 0.722392255 -0.89105928 -0.06156504
## [123,] 0.645027737 -0.16638279 -0.02433375
## [124,] 0.455595663 1.86447739 0.10203627
## [125,] 0.671628560 -0.01859406 0.01499970
## [126,] 0.763878228 -0.74218313 -0.01246680
## [127,] 0.477629514 1.93911988 0.12528896
## [128,] 0.631183045 0.78181233 0.08524846
## [129,] 0.646655948 0.63687704 0.07780221
## [130,] 0.871013049 -1.46468479 -0.03016853
## [131,] 0.662947323 0.93041872 0.11939621
## [132,] 0.662947323 0.93041872 0.11939621
## [133,] 0.732575389 0.27820988 0.08588805
## [134,] 0.857168356 -0.51648966 0.07941368
## [135,] 0.639959955 1.65862723 0.20087233
## [136,] 0.858574580 -0.22403540 0.11124291
## [137,] 0.773473611 0.57310874 0.15219733
## [138,] 0.937345321 -0.65625762 0.10584085
## [139,] 0.965130380 -0.72682019 0.10669679
## [140,] 1.034170693 -1.23300632 0.09039967
## [141,] 0.887178110 0.14387901 0.16113912
## [142,] 0.891157330 0.36304797 0.19443092
## [143,] 1.006616354 -0.57794405 0.15579503
## [144,] 0.714625163 2.32225816 0.31189211
## [145,] 0.863611722 1.09180438 0.25577085
## [146,] 1.218900750 -2.09568476 0.10171796
## [147,] 0.948124939 0.44068296 0.23202747
## [148,] 0.948124939 0.44068296 0.23202747
## [149,] 1.095927262 -0.57141953 0.21438371
## [150,] 1.165555327 -1.22362837 0.18087555
## [151,] 1.007069060 0.51736121 0.29235306
## [152,] 1.045751319 0.15502297 0.27373742
## [153,] 1.099906481 -0.35225058 0.24767551
## [154,] 1.138588740 -0.71458882 0.22905987
## [155,] 0.953135885 1.53544032 0.38872169
## [156,] 1.076919113 0.37595793 0.32915163
## [157,] 1.212418012 -0.63682315 0.29915024
## [158,] 1.266573174 -1.14409669 0.27308834
## [159,] 1.046195293 1.17663409 0.41435088
## [160,] 1.030722390 1.32156939 0.42179713
## [161,] 1.169978521 0.01715170 0.35478082
## [162,] 1.010904502 1.90416401 0.48346936
## [163,] 1.118627074 1.03563964 0.44855660
## [164,] 1.180518688 0.45589844 0.41877157
## [165,] 1.331490491 -0.70181793 0.38132392
## [166,] 1.470746622 -2.00623561 0.31430760
## [167,] 1.424327912 -1.57142972 0.33664637
## [168,] 1.272990344 0.24311493 0.46161179
## [169,] 1.496759692 -1.71242417 0.37085209
## [170,] 1.365240013 -0.48047414 0.43414528
## [171,] 1.195038075 1.11381414 0.51605412
## [172,] 1.334294206 -0.19060354 0.44903780
## [173,] 1.256929689 0.53407295 0.48626908
## [174,] 1.512232596 -1.85735947 0.36340583
## [175,] 1.380712916 -0.62540944 0.42669902
## [176,] 1.256929689 0.53407295 0.48626908
## [177,] 1.597768807 -1.70658663 0.46712031
## [178,] 1.303783641 1.04718404 0.60859920
## [179,] 1.473985580 -0.54710424 0.52669037
## [180,] 1.312329833 1.33949923 0.65797176
## [181,] 1.412315953 0.54344251 0.62678213
## [182,] 1.427201104 0.54452993 0.63654691
## [183,] 1.380782394 0.97933583 0.65888568
## [184,] 1.605139494 -1.12222600 0.55091495
## [185,] 1.589666591 -0.97729070 0.55836120
## [186,] 1.574193687 -0.83235540 0.56580746
## [187,] 1.419464653 0.61699758 0.64027004
## [188,] 1.588704342 -0.24813384 0.66714544
## [189,] 1.619650149 -0.53800444 0.65225292
## [190,] 1.666068859 -0.97281033 0.62991415
## [191,] 1.488130469 0.69394560 0.71554612
## [192,] 1.580967890 -0.17566619 0.67086857
## [193,] 1.598648024 0.26294148 0.75240266
## [194,] 1.598648024 0.26294148 0.75240266
## [195,] 1.621857380 0.04553853 0.74123327
## [196,] 1.691485445 -0.60667031 0.70772511
## [197,] 1.660539638 -0.31679971 0.72261763
b_data_pca$x
## PC1 PC2 PC3
## [1,] -6.018762029 -0.40221757 3.59191907
## [2,] -5.028184548 -1.94155766 2.71486049
## [3,] -3.373832285 -1.09131018 1.04572055
## [4,] -3.327800487 0.31487183 0.94731796
## [5,] -3.397990109 1.33418580 0.98587088
## [6,] -3.140640833 -0.46865024 0.85329324
## [7,] -2.991383577 0.58541427 0.67145370
## [8,] -2.955827138 0.73716061 0.65236480
## [9,] -2.556421699 -0.52733082 0.34879229
## [10,] -2.489884525 -0.37067853 0.29858916
## [11,] -2.487890549 -0.22424698 0.31320735
## [12,] -2.295032079 -1.59513894 0.22111845
## [13,] -2.519924539 1.09461044 0.32196766
## [14,] -2.180073486 -1.65316685 0.15913931
## [15,] -2.108224408 -0.24289654 0.03480820
## [16,] -1.770885226 -2.40152955 -0.15787072
## [17,] -1.998254628 1.17214065 -0.10309380
## [18,] -1.789370431 -0.78448587 -0.20361828
## [19,] -1.867910453 0.23223606 -0.13196492
## [20,] -1.855572101 0.52769120 -0.13582900
## [21,] -1.781350867 0.16971101 -0.16542268
## [22,] -1.647776087 -0.39994851 -0.24248568
## [23,] -1.470303199 -0.88896378 -0.36768261
## [24,] -1.398602569 -0.73149382 -0.42307143
## [25,] -1.525494151 1.08946142 -0.37208548
## [26,] -1.154732220 -2.24296302 -0.53358463
## [27,] -1.428616386 0.95487756 -0.41185923
## [28,] -1.367233935 1.18440633 -0.46093207
## [29,] -1.321376780 1.11670557 -0.47822609
## [30,] -1.095025704 -0.83842471 -0.57157864
## [31,] -1.260643206 0.97639809 -0.48169990
## [32,] -1.291589013 1.26626868 -0.46680739
## [33,] -1.313392145 1.77612589 -0.42380878
## [34,] -0.898714642 -1.32826602 -0.64155270
## [35,] -1.079813780 0.55779794 -0.54017227
## [36,] -0.901875390 -1.10895799 -0.62580424
## [37,] -0.683848518 -2.84559790 -0.69822262
## [38,] -0.823657472 -1.10038095 -0.63021697
## [39,] -0.945429260 0.35292126 -0.56413958
## [40,] -0.850589131 -0.29656484 -0.59825437
## [41,] -0.895005134 0.35836674 -0.56535284
## [42,] -0.879532230 0.21343144 -0.57279910
## [43,] -0.921962989 0.94110043 -0.52122395
## [44,] -0.891017182 0.65122983 -0.53611647
## [45,] -0.569817245 -1.87969241 -0.66763924
## [46,] -0.885009058 1.31160689 -0.50442819
## [47,] -0.929433793 1.89284433 -0.46747124
## [48,] -0.651483086 -0.34888590 -0.59645912
## [49,] -0.783581785 1.10278099 -0.52001032
## [50,] -0.701641564 0.52494488 -0.54521627
## [51,] -0.555228001 -0.63222360 -0.60280011
## [52,] -0.602225732 0.02229915 -0.56730573
## [53,] -0.442920993 -1.28021345 -0.62974297
## [54,] -0.567291973 0.02529165 -0.55296187
## [55,] -0.591062884 0.60979973 -0.53674773
## [56,] -0.552968378 0.39348420 -0.53815234
## [57,] -0.566447305 0.68485105 -0.51608789
## [58,] -0.342677957 -1.27068806 -0.60684759
## [59,] -0.353566424 -0.90521825 -0.59143143
## [60,] -0.305153738 -1.19359259 -0.59915201
## [61,] -0.519780411 0.98193313 -0.48028622
## [62,] -0.339839313 -0.46469711 -0.55535543
## [63,] -0.291426627 -0.75307146 -0.56307601
## [64,] -0.446743414 0.84230424 -0.47140240
## [65,] -0.426694807 0.84420932 -0.46682332
## [66,] -0.449904162 1.06161226 -0.45565394
## [67,] -0.319559986 0.12170766 -0.48452505
## [68,] -0.384612348 0.92075688 -0.43899155
## [69,] -0.243362241 -0.23722925 -0.49138969
## [70,] -0.231050086 -0.16285653 -0.48308748
## [71,] -0.107854610 -1.17631619 -0.52544651
## [72,] -0.154852340 -0.52179344 -0.48995212
## [73,] -0.201271051 -0.08698755 -0.46761335
## [74,] 0.073492712 -2.33049217 -0.56868649
## [75,] -0.050290516 -1.17100979 -0.50911642
## [76,] -0.084993555 -0.58950258 -0.45720898
## [77,] -0.302201956 1.58561431 -0.33575033
## [78,] -0.201628084 0.64353487 -0.38415101
## [79,] -0.019710474 -0.80405210 -0.43649117
## [80,] -0.113126915 0.28527654 -0.37865801
## [81,] -0.185915729 1.15679341 -0.32940139
## [82,] 0.019816452 -0.50683095 -0.41823284
## [83,] -0.047808905 0.36550358 -0.37416192
## [84,] 0.075386570 -0.64795609 -0.41652094
## [85,] 0.106332377 -0.93782669 -0.43141346
## [86,] 0.002001273 0.29588935 -0.34599785
## [87,] 0.118048049 -0.79112538 -0.40184479
## [88,] 0.147818351 -0.78895054 -0.38231522
## [89,] 0.010556196 0.66189869 -0.30068072
## [90,] 0.103393617 -0.20771310 -0.34535826
## [91,] 0.064711358 0.15462514 -0.32674262
## [92,] 0.184158334 -0.49350378 -0.33614214
## [93,] 0.119105972 0.30554544 -0.29060865
## [94,] 0.182991561 -0.12776421 -0.30577549
## [95,] 0.020526075 1.39405642 -0.22758979
## [96,] 0.128836399 0.37950934 -0.27971359
## [97,] 0.036808718 1.61390397 -0.18194035
## [98,] 0.090963880 1.10663043 -0.20800225
## [99,] 0.053687845 1.76142293 -0.15755738
## [100,] 0.246520118 0.16944856 -0.23748000
## [101,] 0.248514094 0.31588011 -0.22286181
## [102,] 0.380033774 -0.91606992 -0.28615500
## [103,] 0.278284397 0.31805495 -0.20333225
## [104,] 0.269960193 0.53654532 -0.18239808
## [105,] 0.331851807 -0.04319588 -0.21218311
## [106,] 0.454459531 -0.91063283 -0.23733109
## [107,] 0.376507261 -0.03993362 -0.18288877
## [108,] 0.267609185 1.12063619 -0.11355393
## [109,] 0.321764347 0.61336264 -0.13961583
## [110,] 0.445769562 -0.03531418 -0.12887916
## [111,] 0.630856651 -1.62851504 -0.20102321
## [112,] 0.470385141 0.03973714 -0.10821932
## [113,] 0.578107713 -0.82878723 -0.14313208
## [114,] 0.389272123 1.12974437 -0.03802853
## [115,] 0.404745027 0.98480907 -0.04547479
## [116,] 0.455142957 0.76917213 -0.03452176
## [117,] 0.547392625 0.04558306 -0.06198827
## [118,] 0.624169391 -0.53307071 -0.08200852
## [119,] 0.646790994 -0.60445094 -0.07596686
## [120,] 0.584311628 0.12131297 -0.02897080
## [121,] 0.398049034 2.00655926 0.07759534
## [122,] 0.722392255 -0.89105928 -0.06156504
## [123,] 0.645027737 -0.16638279 -0.02433375
## [124,] 0.455595663 1.86447739 0.10203627
## [125,] 0.671628560 -0.01859406 0.01499970
## [126,] 0.763878228 -0.74218313 -0.01246680
## [127,] 0.477629514 1.93911988 0.12528896
## [128,] 0.631183045 0.78181233 0.08524846
## [129,] 0.646655948 0.63687704 0.07780221
## [130,] 0.871013049 -1.46468479 -0.03016853
## [131,] 0.662947323 0.93041872 0.11939621
## [132,] 0.662947323 0.93041872 0.11939621
## [133,] 0.732575389 0.27820988 0.08588805
## [134,] 0.857168356 -0.51648966 0.07941368
## [135,] 0.639959955 1.65862723 0.20087233
## [136,] 0.858574580 -0.22403540 0.11124291
## [137,] 0.773473611 0.57310874 0.15219733
## [138,] 0.937345321 -0.65625762 0.10584085
## [139,] 0.965130380 -0.72682019 0.10669679
## [140,] 1.034170693 -1.23300632 0.09039967
## [141,] 0.887178110 0.14387901 0.16113912
## [142,] 0.891157330 0.36304797 0.19443092
## [143,] 1.006616354 -0.57794405 0.15579503
## [144,] 0.714625163 2.32225816 0.31189211
## [145,] 0.863611722 1.09180438 0.25577085
## [146,] 1.218900750 -2.09568476 0.10171796
## [147,] 0.948124939 0.44068296 0.23202747
## [148,] 0.948124939 0.44068296 0.23202747
## [149,] 1.095927262 -0.57141953 0.21438371
## [150,] 1.165555327 -1.22362837 0.18087555
## [151,] 1.007069060 0.51736121 0.29235306
## [152,] 1.045751319 0.15502297 0.27373742
## [153,] 1.099906481 -0.35225058 0.24767551
## [154,] 1.138588740 -0.71458882 0.22905987
## [155,] 0.953135885 1.53544032 0.38872169
## [156,] 1.076919113 0.37595793 0.32915163
## [157,] 1.212418012 -0.63682315 0.29915024
## [158,] 1.266573174 -1.14409669 0.27308834
## [159,] 1.046195293 1.17663409 0.41435088
## [160,] 1.030722390 1.32156939 0.42179713
## [161,] 1.169978521 0.01715170 0.35478082
## [162,] 1.010904502 1.90416401 0.48346936
## [163,] 1.118627074 1.03563964 0.44855660
## [164,] 1.180518688 0.45589844 0.41877157
## [165,] 1.331490491 -0.70181793 0.38132392
## [166,] 1.470746622 -2.00623561 0.31430760
## [167,] 1.424327912 -1.57142972 0.33664637
## [168,] 1.272990344 0.24311493 0.46161179
## [169,] 1.496759692 -1.71242417 0.37085209
## [170,] 1.365240013 -0.48047414 0.43414528
## [171,] 1.195038075 1.11381414 0.51605412
## [172,] 1.334294206 -0.19060354 0.44903780
## [173,] 1.256929689 0.53407295 0.48626908
## [174,] 1.512232596 -1.85735947 0.36340583
## [175,] 1.380712916 -0.62540944 0.42669902
## [176,] 1.256929689 0.53407295 0.48626908
## [177,] 1.597768807 -1.70658663 0.46712031
## [178,] 1.303783641 1.04718404 0.60859920
## [179,] 1.473985580 -0.54710424 0.52669037
## [180,] 1.312329833 1.33949923 0.65797176
## [181,] 1.412315953 0.54344251 0.62678213
## [182,] 1.427201104 0.54452993 0.63654691
## [183,] 1.380782394 0.97933583 0.65888568
## [184,] 1.605139494 -1.12222600 0.55091495
## [185,] 1.589666591 -0.97729070 0.55836120
## [186,] 1.574193687 -0.83235540 0.56580746
## [187,] 1.419464653 0.61699758 0.64027004
## [188,] 1.588704342 -0.24813384 0.66714544
## [189,] 1.619650149 -0.53800444 0.65225292
## [190,] 1.666068859 -0.97281033 0.62991415
## [191,] 1.488130469 0.69394560 0.71554612
## [192,] 1.580967890 -0.17566619 0.67086857
## [193,] 1.598648024 0.26294148 0.75240266
## [194,] 1.598648024 0.26294148 0.75240266
## [195,] 1.621857380 0.04553853 0.74123327
## [196,] 1.691485445 -0.60667031 0.70772511
## [197,] 1.660539638 -0.31679971 0.72261763
plot(b_data_pca$x,xlim=xlim,ylim=xlim)
b_data_pca$rotation[,1]
## rank age finalWorth
## 0.7050171 -0.1060159 -0.7012215
b_data_pca$rotation
## PC1 PC2 PC3
## rank 0.7050171 0.03888488 0.7081235
## age -0.1060159 0.99305470 0.0510196
## finalWorth -0.7012215 -0.11104201 0.7042430
plot(b_data[,excluded_columns_2])
b_data_pca$x
## PC1 PC2 PC3
## [1,] -6.018762029 -0.40221757 3.59191907
## [2,] -5.028184548 -1.94155766 2.71486049
## [3,] -3.373832285 -1.09131018 1.04572055
## [4,] -3.327800487 0.31487183 0.94731796
## [5,] -3.397990109 1.33418580 0.98587088
## [6,] -3.140640833 -0.46865024 0.85329324
## [7,] -2.991383577 0.58541427 0.67145370
## [8,] -2.955827138 0.73716061 0.65236480
## [9,] -2.556421699 -0.52733082 0.34879229
## [10,] -2.489884525 -0.37067853 0.29858916
## [11,] -2.487890549 -0.22424698 0.31320735
## [12,] -2.295032079 -1.59513894 0.22111845
## [13,] -2.519924539 1.09461044 0.32196766
## [14,] -2.180073486 -1.65316685 0.15913931
## [15,] -2.108224408 -0.24289654 0.03480820
## [16,] -1.770885226 -2.40152955 -0.15787072
## [17,] -1.998254628 1.17214065 -0.10309380
## [18,] -1.789370431 -0.78448587 -0.20361828
## [19,] -1.867910453 0.23223606 -0.13196492
## [20,] -1.855572101 0.52769120 -0.13582900
## [21,] -1.781350867 0.16971101 -0.16542268
## [22,] -1.647776087 -0.39994851 -0.24248568
## [23,] -1.470303199 -0.88896378 -0.36768261
## [24,] -1.398602569 -0.73149382 -0.42307143
## [25,] -1.525494151 1.08946142 -0.37208548
## [26,] -1.154732220 -2.24296302 -0.53358463
## [27,] -1.428616386 0.95487756 -0.41185923
## [28,] -1.367233935 1.18440633 -0.46093207
## [29,] -1.321376780 1.11670557 -0.47822609
## [30,] -1.095025704 -0.83842471 -0.57157864
## [31,] -1.260643206 0.97639809 -0.48169990
## [32,] -1.291589013 1.26626868 -0.46680739
## [33,] -1.313392145 1.77612589 -0.42380878
## [34,] -0.898714642 -1.32826602 -0.64155270
## [35,] -1.079813780 0.55779794 -0.54017227
## [36,] -0.901875390 -1.10895799 -0.62580424
## [37,] -0.683848518 -2.84559790 -0.69822262
## [38,] -0.823657472 -1.10038095 -0.63021697
## [39,] -0.945429260 0.35292126 -0.56413958
## [40,] -0.850589131 -0.29656484 -0.59825437
## [41,] -0.895005134 0.35836674 -0.56535284
## [42,] -0.879532230 0.21343144 -0.57279910
## [43,] -0.921962989 0.94110043 -0.52122395
## [44,] -0.891017182 0.65122983 -0.53611647
## [45,] -0.569817245 -1.87969241 -0.66763924
## [46,] -0.885009058 1.31160689 -0.50442819
## [47,] -0.929433793 1.89284433 -0.46747124
## [48,] -0.651483086 -0.34888590 -0.59645912
## [49,] -0.783581785 1.10278099 -0.52001032
## [50,] -0.701641564 0.52494488 -0.54521627
## [51,] -0.555228001 -0.63222360 -0.60280011
## [52,] -0.602225732 0.02229915 -0.56730573
## [53,] -0.442920993 -1.28021345 -0.62974297
## [54,] -0.567291973 0.02529165 -0.55296187
## [55,] -0.591062884 0.60979973 -0.53674773
## [56,] -0.552968378 0.39348420 -0.53815234
## [57,] -0.566447305 0.68485105 -0.51608789
## [58,] -0.342677957 -1.27068806 -0.60684759
## [59,] -0.353566424 -0.90521825 -0.59143143
## [60,] -0.305153738 -1.19359259 -0.59915201
## [61,] -0.519780411 0.98193313 -0.48028622
## [62,] -0.339839313 -0.46469711 -0.55535543
## [63,] -0.291426627 -0.75307146 -0.56307601
## [64,] -0.446743414 0.84230424 -0.47140240
## [65,] -0.426694807 0.84420932 -0.46682332
## [66,] -0.449904162 1.06161226 -0.45565394
## [67,] -0.319559986 0.12170766 -0.48452505
## [68,] -0.384612348 0.92075688 -0.43899155
## [69,] -0.243362241 -0.23722925 -0.49138969
## [70,] -0.231050086 -0.16285653 -0.48308748
## [71,] -0.107854610 -1.17631619 -0.52544651
## [72,] -0.154852340 -0.52179344 -0.48995212
## [73,] -0.201271051 -0.08698755 -0.46761335
## [74,] 0.073492712 -2.33049217 -0.56868649
## [75,] -0.050290516 -1.17100979 -0.50911642
## [76,] -0.084993555 -0.58950258 -0.45720898
## [77,] -0.302201956 1.58561431 -0.33575033
## [78,] -0.201628084 0.64353487 -0.38415101
## [79,] -0.019710474 -0.80405210 -0.43649117
## [80,] -0.113126915 0.28527654 -0.37865801
## [81,] -0.185915729 1.15679341 -0.32940139
## [82,] 0.019816452 -0.50683095 -0.41823284
## [83,] -0.047808905 0.36550358 -0.37416192
## [84,] 0.075386570 -0.64795609 -0.41652094
## [85,] 0.106332377 -0.93782669 -0.43141346
## [86,] 0.002001273 0.29588935 -0.34599785
## [87,] 0.118048049 -0.79112538 -0.40184479
## [88,] 0.147818351 -0.78895054 -0.38231522
## [89,] 0.010556196 0.66189869 -0.30068072
## [90,] 0.103393617 -0.20771310 -0.34535826
## [91,] 0.064711358 0.15462514 -0.32674262
## [92,] 0.184158334 -0.49350378 -0.33614214
## [93,] 0.119105972 0.30554544 -0.29060865
## [94,] 0.182991561 -0.12776421 -0.30577549
## [95,] 0.020526075 1.39405642 -0.22758979
## [96,] 0.128836399 0.37950934 -0.27971359
## [97,] 0.036808718 1.61390397 -0.18194035
## [98,] 0.090963880 1.10663043 -0.20800225
## [99,] 0.053687845 1.76142293 -0.15755738
## [100,] 0.246520118 0.16944856 -0.23748000
## [101,] 0.248514094 0.31588011 -0.22286181
## [102,] 0.380033774 -0.91606992 -0.28615500
## [103,] 0.278284397 0.31805495 -0.20333225
## [104,] 0.269960193 0.53654532 -0.18239808
## [105,] 0.331851807 -0.04319588 -0.21218311
## [106,] 0.454459531 -0.91063283 -0.23733109
## [107,] 0.376507261 -0.03993362 -0.18288877
## [108,] 0.267609185 1.12063619 -0.11355393
## [109,] 0.321764347 0.61336264 -0.13961583
## [110,] 0.445769562 -0.03531418 -0.12887916
## [111,] 0.630856651 -1.62851504 -0.20102321
## [112,] 0.470385141 0.03973714 -0.10821932
## [113,] 0.578107713 -0.82878723 -0.14313208
## [114,] 0.389272123 1.12974437 -0.03802853
## [115,] 0.404745027 0.98480907 -0.04547479
## [116,] 0.455142957 0.76917213 -0.03452176
## [117,] 0.547392625 0.04558306 -0.06198827
## [118,] 0.624169391 -0.53307071 -0.08200852
## [119,] 0.646790994 -0.60445094 -0.07596686
## [120,] 0.584311628 0.12131297 -0.02897080
## [121,] 0.398049034 2.00655926 0.07759534
## [122,] 0.722392255 -0.89105928 -0.06156504
## [123,] 0.645027737 -0.16638279 -0.02433375
## [124,] 0.455595663 1.86447739 0.10203627
## [125,] 0.671628560 -0.01859406 0.01499970
## [126,] 0.763878228 -0.74218313 -0.01246680
## [127,] 0.477629514 1.93911988 0.12528896
## [128,] 0.631183045 0.78181233 0.08524846
## [129,] 0.646655948 0.63687704 0.07780221
## [130,] 0.871013049 -1.46468479 -0.03016853
## [131,] 0.662947323 0.93041872 0.11939621
## [132,] 0.662947323 0.93041872 0.11939621
## [133,] 0.732575389 0.27820988 0.08588805
## [134,] 0.857168356 -0.51648966 0.07941368
## [135,] 0.639959955 1.65862723 0.20087233
## [136,] 0.858574580 -0.22403540 0.11124291
## [137,] 0.773473611 0.57310874 0.15219733
## [138,] 0.937345321 -0.65625762 0.10584085
## [139,] 0.965130380 -0.72682019 0.10669679
## [140,] 1.034170693 -1.23300632 0.09039967
## [141,] 0.887178110 0.14387901 0.16113912
## [142,] 0.891157330 0.36304797 0.19443092
## [143,] 1.006616354 -0.57794405 0.15579503
## [144,] 0.714625163 2.32225816 0.31189211
## [145,] 0.863611722 1.09180438 0.25577085
## [146,] 1.218900750 -2.09568476 0.10171796
## [147,] 0.948124939 0.44068296 0.23202747
## [148,] 0.948124939 0.44068296 0.23202747
## [149,] 1.095927262 -0.57141953 0.21438371
## [150,] 1.165555327 -1.22362837 0.18087555
## [151,] 1.007069060 0.51736121 0.29235306
## [152,] 1.045751319 0.15502297 0.27373742
## [153,] 1.099906481 -0.35225058 0.24767551
## [154,] 1.138588740 -0.71458882 0.22905987
## [155,] 0.953135885 1.53544032 0.38872169
## [156,] 1.076919113 0.37595793 0.32915163
## [157,] 1.212418012 -0.63682315 0.29915024
## [158,] 1.266573174 -1.14409669 0.27308834
## [159,] 1.046195293 1.17663409 0.41435088
## [160,] 1.030722390 1.32156939 0.42179713
## [161,] 1.169978521 0.01715170 0.35478082
## [162,] 1.010904502 1.90416401 0.48346936
## [163,] 1.118627074 1.03563964 0.44855660
## [164,] 1.180518688 0.45589844 0.41877157
## [165,] 1.331490491 -0.70181793 0.38132392
## [166,] 1.470746622 -2.00623561 0.31430760
## [167,] 1.424327912 -1.57142972 0.33664637
## [168,] 1.272990344 0.24311493 0.46161179
## [169,] 1.496759692 -1.71242417 0.37085209
## [170,] 1.365240013 -0.48047414 0.43414528
## [171,] 1.195038075 1.11381414 0.51605412
## [172,] 1.334294206 -0.19060354 0.44903780
## [173,] 1.256929689 0.53407295 0.48626908
## [174,] 1.512232596 -1.85735947 0.36340583
## [175,] 1.380712916 -0.62540944 0.42669902
## [176,] 1.256929689 0.53407295 0.48626908
## [177,] 1.597768807 -1.70658663 0.46712031
## [178,] 1.303783641 1.04718404 0.60859920
## [179,] 1.473985580 -0.54710424 0.52669037
## [180,] 1.312329833 1.33949923 0.65797176
## [181,] 1.412315953 0.54344251 0.62678213
## [182,] 1.427201104 0.54452993 0.63654691
## [183,] 1.380782394 0.97933583 0.65888568
## [184,] 1.605139494 -1.12222600 0.55091495
## [185,] 1.589666591 -0.97729070 0.55836120
## [186,] 1.574193687 -0.83235540 0.56580746
## [187,] 1.419464653 0.61699758 0.64027004
## [188,] 1.588704342 -0.24813384 0.66714544
## [189,] 1.619650149 -0.53800444 0.65225292
## [190,] 1.666068859 -0.97281033 0.62991415
## [191,] 1.488130469 0.69394560 0.71554612
## [192,] 1.580967890 -0.17566619 0.67086857
## [193,] 1.598648024 0.26294148 0.75240266
## [194,] 1.598648024 0.26294148 0.75240266
## [195,] 1.621857380 0.04553853 0.74123327
## [196,] 1.691485445 -0.60667031 0.70772511
## [197,] 1.660539638 -0.31679971 0.72261763
plot(b_data_pca)
#Explain the variate representation each PCs (4 points)
#get the original value of the data based on PCA
center <- b_data_pca$center
center
## rank age finalWorth
## 99.29949 68.21827 26448.73096
scale <- b_data_pca$scale
scale
## rank age finalWorth
## 57.30251 13.70342 27160.93497
new_b_data <- as.matrix(b_data[,excluded_columns])
new_b_data
## rank age finalWorth
## [1,] 1 74 211000
## [2,] 2 51 180000
## [3,] 3 59 114000
## [4,] 4 78 107000
## [5,] 5 92 106000
## [6,] 6 67 104000
## [7,] 7 81 94500
## [8,] 8 83 93000
## [9,] 9 65 83400
## [10,] 10 67 80700
## [11,] 11 69 80500
## [12,] 12 50 79200
## [13,] 13 87 77300
## [14,] 14 49 76000
## [15,] 15 68 68000
## [16,] 16 38 64400
## [17,] 17 87 59000
## [18,] 17 60 59000
## [19,] 19 74 58800
## [20,] 20 78 57600
## [21,] 21 73 56700
## [22,] 22 65 54400
## [23,] 23 58 50100
## [24,] 24 60 47200
## [25,] 25 85 45100
## [26,] 26 39 45000
## [27,] 27 83 42900
## [28,] 28 86 40100
## [29,] 29 85 39100
## [30,] 30 58 38900
## [31,] 31 83 38300
## [32,] 31 87 38300
## [33,] 33 94 38000
## [34,] 34 51 35300
## [35,] 35 77 35000
## [36,] 35 54 35000
## [37,] 37 30 34700
## [38,] 38 54 33400
## [39,] 39 74 32600
## [40,] 40 65 32100
## [41,] 41 74 31600
## [42,] 41 72 31600
## [43,] 43 82 31200
## [44,] 43 78 31200
## [45,] 45 43 30200
## [46,] 46 87 29700
## [47,] 47 95 29500
## [48,] 48 64 28500
## [49,] 49 84 28100
## [50,] 50 76 27800
## [51,] 51 60 27400
## [52,] 52 69 27000
## [53,] 53 51 26700
## [54,] 54 69 26600
## [55,] 55 77 25600
## [56,] 56 74 25500
## [57,] 57 78 25300
## [58,] 58 51 25200
## [59,] 59 56 24600
## [60,] 60 52 24400
## [61,] 61 82 24200
## [62,] 62 62 23700
## [63,] 63 58 23500
## [64,] 64 80 23400
## [65,] 65 80 23100
## [66,] 65 83 23100
## [67,] 67 70 22900
## [68,] 68 81 22600
## [69,] 69 65 22400
## [70,] 70 66 22100
## [71,] 71 52 22000
## [72,] 72 61 21600
## [73,] 72 67 21600
## [74,] 74 36 21200
## [75,] 74 52 21200
## [76,] 76 60 21100
## [77,] 77 90 21000
## [78,] 77 77 21000
## [79,] 79 57 20900
## [80,] 80 72 20500
## [81,] 81 84 20200
## [82,] 82 61 19600
## [83,] 83 73 19100
## [84,] 84 59 19000
## [85,] 84 55 19000
## [86,] 86 72 18900
## [87,] 86 57 18900
## [88,] 88 57 18700
## [89,] 89 77 18500
## [90,] 89 65 18500
## [91,] 89 70 18500
## [92,] 92 61 18000
## [93,] 93 72 17700
## [94,] 94 66 17500
## [95,] 94 87 17500
## [96,] 94 73 17500
## [97,] 97 90 17400
## [98,] 97 83 17400
## [99,] 99 92 17100
## [100,] 100 70 16700
## [101,] 101 72 16500
## [102,] 101 55 16500
## [103,] 103 72 16300
## [104,] 104 75 16200
## [105,] 104 67 16200
## [106,] 106 55 16000
## [107,] 107 67 15900
## [108,] 108 83 15800
## [109,] 108 76 15800
## [110,] 112 67 15600
## [111,] 113 45 15500
## [112,] 114 68 15300
## [113,] 115 56 15200
## [114,] 116 83 14900
## [115,] 116 81 14900
## [116,] 118 78 14800
## [117,] 119 68 14700
## [118,] 120 60 14600
## [119,] 121 59 14500
## [120,] 122 69 14400
## [121,] 123 95 14300
## [122,] 124 55 14200
## [123,] 124 65 14200
## [124,] 126 93 14100
## [125,] 127 67 14000
## [126,] 128 57 13900
## [127,] 128 94 13900
## [128,] 130 78 13700
## [129,] 130 76 13700
## [130,] 130 47 13700
## [131,] 133 80 13300
## [132,] 133 80 13300
## [133,] 133 71 13300
## [134,] 136 60 13200
## [135,] 137 90 13100
## [136,] 138 64 12900
## [137,] 138 75 12900
## [138,] 140 58 12600
## [139,] 141 57 12300
## [140,] 142 50 12200
## [141,] 142 69 12200
## [142,] 144 72 12100
## [143,] 145 59 12000
## [144,] 146 99 11800
## [145,] 147 82 11600
## [146,] 148 38 11500
## [147,] 148 73 11500
## [148,] 148 73 11500
## [149,] 151 59 11400
## [150,] 151 50 11400
## [151,] 153 74 11300
## [152,] 153 69 11300
## [153,] 153 62 11300
## [154,] 153 57 11300
## [155,] 157 88 11100
## [156,] 157 72 11100
## [157,] 159 58 11000
## [158,] 159 51 11000
## [159,] 161 83 10900
## [160,] 161 85 10900
## [161,] 161 67 10900
## [162,] 164 93 10700
## [163,] 165 81 10600
## [164,] 165 73 10600
## [165,] 167 57 10500
## [166,] 167 39 10500
## [167,] 167 45 10500
## [168,] 170 70 10300
## [169,] 171 43 10200
## [170,] 171 60 10200
## [171,] 171 82 10200
## [172,] 171 64 10200
## [173,] 171 74 10200
## [174,] 171 41 10200
## [175,] 171 58 10200
## [176,] 171 74 10200
## [177,] 179 43 10100
## [178,] 179 81 10100
## [179,] 179 59 10100
## [180,] 182 85 10000
## [181,] 183 74 9900
## [182,] 184 74 9800
## [183,] 184 80 9800
## [184,] 184 51 9800
## [185,] 184 53 9800
## [186,] 184 55 9800
## [187,] 184 75 9800
## [188,] 190 63 9700
## [189,] 190 59 9700
## [190,] 190 53 9700
## [191,] 190 76 9700
## [192,] 190 64 9700
## [193,] 195 70 9600
## [194,] 195 70 9600
## [195,] 195 67 9600
## [196,] 195 58 9600
## [197,] 195 62 9600
drop(scale(new_b_data,center=center, scale=scale)%*%b_data_pca$rotation[,1])
## [1] -6.018762029 -5.028184548 -3.373832285 -3.327800487 -3.397990109
## [6] -3.140640833 -2.991383577 -2.955827138 -2.556421699 -2.489884525
## [11] -2.487890549 -2.295032079 -2.519924539 -2.180073486 -2.108224408
## [16] -1.770885226 -1.998254628 -1.789370431 -1.867910453 -1.855572101
## [21] -1.781350867 -1.647776087 -1.470303199 -1.398602569 -1.525494151
## [26] -1.154732220 -1.428616386 -1.367233935 -1.321376780 -1.095025704
## [31] -1.260643206 -1.291589013 -1.313392145 -0.898714642 -1.079813780
## [36] -0.901875390 -0.683848518 -0.823657472 -0.945429260 -0.850589131
## [41] -0.895005134 -0.879532230 -0.921962989 -0.891017182 -0.569817245
## [46] -0.885009058 -0.929433793 -0.651483086 -0.783581785 -0.701641564
## [51] -0.555228001 -0.602225732 -0.442920993 -0.567291973 -0.591062884
## [56] -0.552968378 -0.566447305 -0.342677957 -0.353566424 -0.305153738
## [61] -0.519780411 -0.339839313 -0.291426627 -0.446743414 -0.426694807
## [66] -0.449904162 -0.319559986 -0.384612348 -0.243362241 -0.231050086
## [71] -0.107854610 -0.154852340 -0.201271051 0.073492712 -0.050290516
## [76] -0.084993555 -0.302201956 -0.201628084 -0.019710474 -0.113126915
## [81] -0.185915729 0.019816452 -0.047808905 0.075386570 0.106332377
## [86] 0.002001273 0.118048049 0.147818351 0.010556196 0.103393617
## [91] 0.064711358 0.184158334 0.119105972 0.182991561 0.020526075
## [96] 0.128836399 0.036808718 0.090963880 0.053687845 0.246520118
## [101] 0.248514094 0.380033774 0.278284397 0.269960193 0.331851807
## [106] 0.454459531 0.376507261 0.267609185 0.321764347 0.445769562
## [111] 0.630856651 0.470385141 0.578107713 0.389272123 0.404745027
## [116] 0.455142957 0.547392625 0.624169391 0.646790994 0.584311628
## [121] 0.398049034 0.722392255 0.645027737 0.455595663 0.671628560
## [126] 0.763878228 0.477629514 0.631183045 0.646655948 0.871013049
## [131] 0.662947323 0.662947323 0.732575389 0.857168356 0.639959955
## [136] 0.858574580 0.773473611 0.937345321 0.965130380 1.034170693
## [141] 0.887178110 0.891157330 1.006616354 0.714625163 0.863611722
## [146] 1.218900750 0.948124939 0.948124939 1.095927262 1.165555327
## [151] 1.007069060 1.045751319 1.099906481 1.138588740 0.953135885
## [156] 1.076919113 1.212418012 1.266573174 1.046195293 1.030722390
## [161] 1.169978521 1.010904502 1.118627074 1.180518688 1.331490491
## [166] 1.470746622 1.424327912 1.272990344 1.496759692 1.365240013
## [171] 1.195038075 1.334294206 1.256929689 1.512232596 1.380712916
## [176] 1.256929689 1.597768807 1.303783641 1.473985580 1.312329833
## [181] 1.412315953 1.427201104 1.380782394 1.605139494 1.589666591
## [186] 1.574193687 1.419464653 1.588704342 1.619650149 1.666068859
## [191] 1.488130469 1.580967890 1.598648024 1.598648024 1.621857380
## [196] 1.691485445 1.660539638
predict(b_data_pca)[,1]
## [1] -6.018762029 -5.028184548 -3.373832285 -3.327800487 -3.397990109
## [6] -3.140640833 -2.991383577 -2.955827138 -2.556421699 -2.489884525
## [11] -2.487890549 -2.295032079 -2.519924539 -2.180073486 -2.108224408
## [16] -1.770885226 -1.998254628 -1.789370431 -1.867910453 -1.855572101
## [21] -1.781350867 -1.647776087 -1.470303199 -1.398602569 -1.525494151
## [26] -1.154732220 -1.428616386 -1.367233935 -1.321376780 -1.095025704
## [31] -1.260643206 -1.291589013 -1.313392145 -0.898714642 -1.079813780
## [36] -0.901875390 -0.683848518 -0.823657472 -0.945429260 -0.850589131
## [41] -0.895005134 -0.879532230 -0.921962989 -0.891017182 -0.569817245
## [46] -0.885009058 -0.929433793 -0.651483086 -0.783581785 -0.701641564
## [51] -0.555228001 -0.602225732 -0.442920993 -0.567291973 -0.591062884
## [56] -0.552968378 -0.566447305 -0.342677957 -0.353566424 -0.305153738
## [61] -0.519780411 -0.339839313 -0.291426627 -0.446743414 -0.426694807
## [66] -0.449904162 -0.319559986 -0.384612348 -0.243362241 -0.231050086
## [71] -0.107854610 -0.154852340 -0.201271051 0.073492712 -0.050290516
## [76] -0.084993555 -0.302201956 -0.201628084 -0.019710474 -0.113126915
## [81] -0.185915729 0.019816452 -0.047808905 0.075386570 0.106332377
## [86] 0.002001273 0.118048049 0.147818351 0.010556196 0.103393617
## [91] 0.064711358 0.184158334 0.119105972 0.182991561 0.020526075
## [96] 0.128836399 0.036808718 0.090963880 0.053687845 0.246520118
## [101] 0.248514094 0.380033774 0.278284397 0.269960193 0.331851807
## [106] 0.454459531 0.376507261 0.267609185 0.321764347 0.445769562
## [111] 0.630856651 0.470385141 0.578107713 0.389272123 0.404745027
## [116] 0.455142957 0.547392625 0.624169391 0.646790994 0.584311628
## [121] 0.398049034 0.722392255 0.645027737 0.455595663 0.671628560
## [126] 0.763878228 0.477629514 0.631183045 0.646655948 0.871013049
## [131] 0.662947323 0.662947323 0.732575389 0.857168356 0.639959955
## [136] 0.858574580 0.773473611 0.937345321 0.965130380 1.034170693
## [141] 0.887178110 0.891157330 1.006616354 0.714625163 0.863611722
## [146] 1.218900750 0.948124939 0.948124939 1.095927262 1.165555327
## [151] 1.007069060 1.045751319 1.099906481 1.138588740 0.953135885
## [156] 1.076919113 1.212418012 1.266573174 1.046195293 1.030722390
## [161] 1.169978521 1.010904502 1.118627074 1.180518688 1.331490491
## [166] 1.470746622 1.424327912 1.272990344 1.496759692 1.365240013
## [171] 1.195038075 1.334294206 1.256929689 1.512232596 1.380712916
## [176] 1.256929689 1.597768807 1.303783641 1.473985580 1.312329833
## [181] 1.412315953 1.427201104 1.380782394 1.605139494 1.589666591
## [186] 1.574193687 1.419464653 1.588704342 1.619650149 1.666068859
## [191] 1.488130469 1.580967890 1.598648024 1.598648024 1.621857380
## [196] 1.691485445 1.660539638
#The aboved two gives us the same thing. predict is a good function to know.
b_data$selfMade <- as.factor(b_data$selfMade)
out <- sapply(1:3, function(i){plot(b_data$selfMade,b_data_pca$x[,i],xlab=paste("PC",i,sep=""),ylab="selfMade")})
pairs(b_data_pca$x[,1:3], ylim = c(-6,4),xlim = c(-6,4),panel=function(x,y,...){text(x,y,b_data$selfMade)})
# Perform some visualization using PCs. (4 points)
library(factoextra)
## Loading required package: ggplot2
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
library(FactoMineR)
library(ggfortify)
library(psych)
##
## Attaching package: 'psych'
##
## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha
##
## The following object is masked from 'package:car':
##
## logit
library(corrplot)
## corrplot 0.92 loaded
library(devtools)
## Loading required package: usethis
# Correlation
pairs.panels(b_data[,excluded_columns],
gap = 0,
bg = c("red", "blue")[b_data$selfMade],
pch=21)
pairs.panels(b_data_pca$x,
gap=0,
bg = c("red", "blue")[b_data$selfMade],
pch=21)
fviz_eig(b_data_pca, addlabels = TRUE)
fviz_pca_var(b_data_pca,col.var = "cos2",
gradient.cols = c("#FFCC00", "#CC9933", "#660033", "#330033"),
repel = TRUE)
fviz_pca_ind(b_data_pca, col.ind = "cos2",
gradient.cols = c("#FFCC00", "#CC9933", "#660033", "#330033"),
repel = TRUE)
biplot(b_data_pca)
autoplot(b_data_pca,
data = b_data[,excluded_columns],
loadings = TRUE,
labels = b_data$selfMade)
# Different PCA Method. ---------------------------------------------
res.pca <- PCA(b_data[,excluded_columns], graph = FALSE)
print(res.pca)
## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 197 individuals, described by 3 variables
## *The results are available in the following objects:
##
## name description
## 1 "$eig" "eigenvalues"
## 2 "$var" "results for the variables"
## 3 "$var$coord" "coord. for the variables"
## 4 "$var$cor" "correlations variables - dimensions"
## 5 "$var$cos2" "cos2 for the variables"
## 6 "$var$contrib" "contributions of the variables"
## 7 "$ind" "results for the individuals"
## 8 "$ind$coord" "coord. for the individuals"
## 9 "$ind$cos2" "cos2 for the individuals"
## 10 "$ind$contrib" "contributions of the individuals"
## 11 "$call" "summary statistics"
## 12 "$call$centre" "mean of the variables"
## 13 "$call$ecart.type" "standard error of the variables"
## 14 "$call$row.w" "weights for the individuals"
## 15 "$call$col.w" "weights for the variables"
# Visualize and Interpret PCA using these functions
#get_eigenvalue(res.pca): Extract the eigenvalues/variances of principal components
#fviz_eig(res.pca): Visualize the eigenvalues
#get_pca_ind(res.pca), get_pca_var(res.pca): Extract the results for individuals and variables, respectively.
#fviz_pca_ind(res.pca), fviz_pca_var(res.pca): Visualize the results individuals and variables, respectively.
#fviz_pca_biplot(res.pca): Make a biplot of individuals and variables.
eig.val <- get_eigenvalue(res.pca)
eig.val
## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 1.7136414 57.121381 57.12138
## Dim.2 0.9937337 33.124456 90.24584
## Dim.3 0.2926249 9.754163 100.00000
fviz_eig(res.pca, addlabels = TRUE, ylim = c(0, 50))
var <- get_pca_var(res.pca)
#var$coord: coordinates of variables to create a scatter plot
#var$cos2: represents the quality of representation for variables on the factor map. It’s calculated as the squared coordinates: var.cos2 = var.coord * var.coord.
#var$contrib: contains the contributions (in percentage) of the variables to the principal components.
#The contribution of a variable (var) to a given principal component is (in percentage) : (var.cos2 * 100) / (total cos2 of the component).
var
## Principal Component Analysis Results for variables
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the variables"
## 2 "$cor" "Correlations between variables and dimensions"
## 3 "$cos2" "Cos2 for the variables"
## 4 "$contrib" "contributions of the variables"
# Coordinates
head(var$coord)
## Dim.1 Dim.2 Dim.3
## rank -0.9229106 0.03876286 0.38305808
## age 0.1387813 0.98993841 0.02759896
## finalWorth 0.9179418 -0.11069355 0.38095893
# Cos2: quality on the factore map
head(var$cos2)
## Dim.1 Dim.2 Dim.3
## rank 0.85176395 0.001502559 0.1467334942
## age 0.01926024 0.979978062 0.0007617025
## finalWorth 0.84261724 0.012253062 0.1451297033
# Contributions to the principal components
head(var$contrib)
## Dim.1 Dim.2 Dim.3
## rank 49.704911 0.1512034 50.14389
## age 1.123936 98.6157639 0.26030
## finalWorth 49.171153 1.2330327 49.59581
#The plot Below is also known as variable correlation plots. It shows the relationships between all variables. It can be interpreted as follow:
#Positively correlated variables are grouped together.
#Negatively correlated variables are positioned on opposite sides of the plot origin (opposed quadrants).
#The distance between variables and the origin measures the quality of the variables on the factor map.
#Variables that are away from the origin are well represented on the factor map.
# Correlation circle
fviz_pca_var(res.pca, col.var = "black")
# Quality of representation
corrplot(var$cos2, is.corr=FALSE)
# Total cos2 of variables on Dim.1 and Dim.2
#A high cos2 indicates a good representation of the variable on the principal component.
#In this case the variable is positioned close to the circumference of the correlation circle.
#A low cos2 indicates that the variable is not perfectly represented by the PCs.
#In this case the variable is close to the center of the circle.
fviz_cos2(res.pca, choice = "var", axes = 1:2)
fviz_pca_var(res.pca, col.var = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping
)
# Change the transparency by cos2 values
fviz_pca_var(res.pca, alpha.var = "cos2")
corrplot(var$contrib, is.corr=FALSE)
# Contributions of variables to PC1
fviz_contrib(res.pca, choice = "var", axes = 1, top = 10)
# Contributions of variables to PC2
fviz_contrib(res.pca, choice = "var", axes = 2, top = 10)
fviz_pca_var(res.pca, col.var = "contrib",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07")
)
fviz_pca_var(res.pca, alpha.var = "contrib")
fviz_pca_ind(res.pca,
geom.ind = "point", # show points only (nbut not "text")
col.ind = b_data$selfMade, # color by groups
palette = c("#00AFBB", "#E7B800", "#FC4E07"),
addEllipses = TRUE, # Concentration ellipses
legend.title = "Groups"
)
# Description of PC
res.desc <- dimdesc(res.pca, axes = c(1,2,3), proba = 0.05)
# Description of dimension 1
res.desc$Dim.1
##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## finalWorth 0.9179418 3.136636e-80
## rank -0.9229106 9.095430e-83
res.desc$Dim.2
##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## age 0.9899384 1.437337e-167
res.desc$Dim.3
##
## Link between the variable and the continuous variables (R-square)
## =================================================================================
## correlation p.value
## rank 0.3830581 2.766070e-08
## finalWorth 0.3809589 3.339011e-08
# Graph of Indiviuals
ind <- get_pca_ind(res.pca)
ind
## Principal Component Analysis Results for individuals
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the individuals"
## 2 "$cos2" "Cos2 for the individuals"
## 3 "$contrib" "contributions of the individuals"
## Principal Component Analysis Results for individuals
## ===================================================
## Name Description
## 1 "$coord" "Coordinates for the individuals"
## 2 "$cos2" "Cos2 for the individuals"
## 3 "$contrib" "contributions of the individuals"
#To get access to the different components, use this:
# Coordinates of individuals
head(ind$coord)
## Dim.1 Dim.2 Dim.3
## 1 6.034096 -0.4032423 3.6010705
## 2 5.040995 -1.9465043 2.7217773
## 3 3.382428 -1.0940906 1.0483848
## 4 3.336279 0.3156740 0.9497315
## 5 3.406647 1.3375850 0.9883827
## 6 3.148642 -0.4698443 0.8554672
# Quality of individuals
head(ind$cos2)
## Dim.1 Dim.2 Dim.3
## 1 0.7349587 0.003282243 0.26175904
## 2 0.6941441 0.103497012 0.20235888
## 3 0.8328492 0.087139647 0.08001118
## 4 0.9174409 0.008213554 0.07434557
## 5 0.8075304 0.124493683 0.06797587
## 6 0.9123383 0.020315011 0.06734665
# Contributions of individuals
head(ind$contrib)
## Dim.1 Dim.2 Dim.3
## 1 10.785451 0.08306078 22.494986
## 2 7.527424 1.93541679 12.850727
## 3 3.388995 0.61146321 1.906619
## 4 3.297149 0.05090278 1.564675
## 5 3.437702 0.91391656 1.694622
## 6 2.936706 0.11276429 1.269490
fviz_pca_ind(res.pca)
fviz_pca_ind(res.pca, col.ind = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping (slow if many points)
)
fviz_pca_ind(res.pca, pointsize = "cos2",
pointshape = 21, fill = "#E7B800",
repel = TRUE # Avoid text overlapping (slow if many points)
)
fviz_pca_ind(res.pca, col.ind = "cos2", pointsize = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping (slow if many points)
)
fviz_cos2(res.pca, choice = "ind")
# Total contribution on PC1 and PC2
fviz_contrib(res.pca, choice = "ind", axes = 1:2)
# Create a random continuous variable of length 23,
# Same length as the number of active individuals in the PCA
set.seed(123)
my.cont.var <- rnorm(197)
# Color individuals by the continuous variable
fviz_pca_ind(res.pca, col.ind = my.cont.var,
gradient.cols = c("blue", "yellow", "red"),
legend.title = "Cont.Var")
fviz_pca_ind(res.pca,
geom.ind = "point", # show points only (nbut not "text")
col.ind = b_data$selfMade, # color by groups
palette = c("#00AFBB", "#E7B800", "#FC4E07"),
addEllipses = TRUE, # Concentration ellipses
legend.title = "Groups"
)
fviz_pca_ind(res.pca, geom.ind = "point", col.ind = b_data$selfMade,
palette = c("#00AFBB", "#E7B800", "#FC4E07"),
addEllipses = TRUE, ellipse.type = "confidence",
legend.title = "Groups"
)
fviz_pca_ind(res.pca,
label = "none", # hide individual labels
habillage = b_data$selfMade, # color by groups
addEllipses = TRUE, # Concentration ellipses
palette = "jco"
)
fviz_pca_var(res.pca, geom.var = c("point", "text"))
# Show individuals text labels only
fviz_pca_ind(res.pca, geom.ind = "text")
# Change the size of arrows an labels
fviz_pca_var(res.pca, arrowsize = 1, labelsize = 5,
repel = TRUE)
# Change points size, shape and fill color
# Change labelsize
fviz_pca_ind(res.pca,
pointsize = 3, pointshape = 21, fill = "lightblue",
labelsize = 5, repel = TRUE)
fviz_pca_ind(res.pca,
geom.ind = "point", # show points only (but not "text")
group.ind = b_data$selfMade, # color by groups
legend.title = "Groups",
mean.point = FALSE)
fviz_pca_ind(res.pca,
geom.ind = "point", # show points only (but not "text")
group.ind = b_data$selfMade, # color by groups
legend.title = "Groups",
mean.point = TRUE)
fviz_pca_var(res.pca, axes.linetype = "blank")
ind.p <- fviz_pca_ind(res.pca, geom = "point", col.ind = b_data$selfMade)
ggpubr::ggpar(ind.p,
title = "Principal Component Analysis",
subtitle = "Iris data set",
caption = "Source: factoextra",
xlab = "PC1", ylab = "PC2",
legend.title = "Survivorship", legend.position = "top",
ggtheme = theme_gray(), palette = "jco"
)
fviz_pca_biplot(res.pca, repel = TRUE,col.ind = b_data$selfMade,
col.var = "#2E9FDF", # Variables color
)
fviz_pca_biplot(res.pca,
col.ind = b_data$selfMade, palette = "jco",
addEllipses = TRUE, label = "var",
col.var = "black", repel = TRUE,
legend.title = "Survivorship")
fviz_pca_biplot(res.pca,
# Fill individuals by groups
geom.ind = "point",
pointshape = 21,
pointsize = 2.5,
fill.ind = b_data$selfMade,
col.ind = "black",
# Color variable by groups
legend.title = list(fill = "Survivorship", color = "Clusters"),
repel = TRUE # Avoid label overplotting
)+
ggpubr::fill_palette("jco")+ # Indiviual fill color
ggpubr::color_palette("npg") # Variable colors
fviz_pca_biplot(res.pca,
# Individuals
geom.ind = "point",
fill.ind = b_data$selfMade, col.ind = "black",
pointshape = 21, pointsize = 2,
palette = "jco",
addEllipses = TRUE,
# Variables
alpha.var ="contrib", col.var = "contrib",
gradient.cols = "RdYlBu",
legend.title = list(fill = "selfMade", color = "Contrib",
alpha = "Contrib")
)
